The document discusses the point-slope formula for writing the equation of a line given a point and slope. It provides examples of using the formula, such as writing the equation of the line through point (3, -2) with slope 5. It also discusses that horizontal lines have a slope of 0 and the equation y=b, since the y-coordinate remains constant while the x-coordinate changes. The slope of a horizontal line is 0 because when calculating slope using two points, the change in y-values is 0.

1. FUNCTIONS
UNIT 4 - HOMEWORK 8
Homework Help

2. POINT-SLOPE FORMULA

3. POINT-SLOPE FORMULA
• Alternatemethod to find the equation of a line with the slope and
one point.

4. POINT-SLOPE FORMULA
• Alternatemethod to find the equation of a line with the slope and
one point.
y − y1 = m ( x − x1 )

5. POINT-SLOPE FORMULA
• Alternatemethod to find the equation of a line with the slope and
one point.
y − y1 = m ( x − x1 )
• The x and y stay the same. Never substitute a value for these.

6. POINT-SLOPE FORMULA
• Alternatemethod to find the equation of a line with the slope and
one point.
y − y1 = m ( x − x1 )
• The x and y stay the same. Never substitute a value for these.
• The x1 and y1 represent the given point. This is where you substitute
the given point.

7. USING POINT-SLOPE FORMULA
Write the point-slope form of
the equation passing through
(3, -2) with a slope of 5.

8. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5.

9. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5.
y − y1 = m ( x − x1 )

10. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5. • Label your given point.
y − y1 = m ( x − x1 )

11. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5. • Label your given point.
( x1, y1 )
y − y1 = m ( x − x1 )

12. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 )

13. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 )
y − ( −2 ) = 5 ( x − 3)

14. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 ) • When the question asks for the
equation in point-slope form, the
y − ( −2 ) = 5 ( x − 3) only simplifying done is to change
any subtracting negatives to
addition.

15. USING POINT-SLOPE FORMULA
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(3, -2) with a slope of 5. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 ) • When the question asks for the
equation in point-slope form, the
y − ( −2 ) = 5 ( x − 3) only simplifying done is to change
any subtracting negatives to
addition.
y + 2 = 5 ( x − 3)

16. YOUR TURN...
Write the point-slope form of
the equation passing through
(7, -3) with a slope of -2.

17. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2.

18. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2.
y − y1 = m ( x − x1 )

19. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2. • Label your given point.
y − y1 = m ( x − x1 )

20. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2. • Label your given point.
( x1, y1 )
y − y1 = m ( x − x1 )

21. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 )

22. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 )
y − ( −3) = −2 ( x − 7 )

23. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 ) • When the question asks for the
equation in point-slope form, the
y − ( −3) = −2 ( x − 7 ) only simplifying is change to
addition any subtraction
negatives.

24. YOUR TURN...
Write the point-slope form of • Write the general formula for
the equation passing through point-slope form.
(7, -3) with a slope of -2. • Label your given point.
( x1, y1 )
• Substitute the slope and point.
y − y1 = m ( x − x1 ) • When the question asks for the
equation in point-slope form, the
y − ( −3) = −2 ( x − 7 ) only simplifying is change to
addition any subtraction
negatives.
y + 3 = −2 ( x − 7 )

25. HORIZONTAL LINES
• Look at the horizon at the right.

26. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.

27. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.

28. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.

29. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)

30. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)
• Why is the slope zero?

31. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)
• Why is the slope zero?
• Suppose you have points (2, 5) and (3, 5). You know they are horizontal
because the x-coordinate changes.

32. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)
• Why is the slope zero?
• Suppose you have points (2, 5) and (3, 5). You know they are horizontal
because the x-coordinate changes.
• Substitute into the slope formula.
y2 − y1
m=
x2 − x1

33. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)
• Why is the slope zero?
• Suppose you have points (2, 5) and (3, 5). You know they are horizontal
because the x-coordinate changes.
• Substitute into the slope formula.
y2 − y1 5 − 5
m= =
x2 − x1 2 − 3

34. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)
• Why is the slope zero?
• Suppose you have points (2, 5) and (3, 5). You know they are horizontal
because the x-coordinate changes.
• Substitute into the slope formula.
y2 − y1 5 − 5 0
m= = =
x2 − x1 2 − 3 −1

35. HORIZONTAL LINES
• Look at the horizon at the right.
• The direction of the horizon is from left to
right. This is how all horizontal lines
appear on a graph.
• The x-coordinate changes but the y-coordinate remains constant.
• Horizontal lines have the equation y = b.
• Slope of all horizontal lines is zero. (Think, y = 0x + b.)
• Why is the slope zero?
• Suppose you have points (2, 5) and (3, 5). You know they are horizontal
because the x-coordinate changes.
• Substitute into the slope formula.
y2 − y1 5 − 5 0
m= = =
x2 − x1 2 − 3 −1
• Zero divided by anything is 0. Therefore, the slope is 0.

36. VERTICAL LINES
• Vertical lines go up and down.

37. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.

38. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis

39. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.

40. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.
• Why is the slope undefined?

41. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.
• Why is the slope undefined?
• Suppose you have points (1, 5) and (1, 3). You know they are
vertical because they have the same x-coordinate.

42. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.
• Why is the slope undefined?
• Suppose you have points (1, 5) and (1, 3). You know they are
vertical because they have the same x-coordinate.
• Substitute into the slope formula.
y2 − y1
m=
x2 − x1

43. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.
• Why is the slope undefined?
• Suppose you have points (1, 5) and (1, 3). You know they are
vertical because they have the same x-coordinate.
• Substitute into the slope formula.
y2 − y1 5 − 3
m= =
x2 − x1 1 − 1

44. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.
• Why is the slope undefined?
• Suppose you have points (1, 5) and (1, 3). You know they are
vertical because they have the same x-coordinate.
• Substitute into the slope formula.
y2 − y1 5 − 3 2
m= = =
x2 − x1 1 − 1 0

45. VERTICAL LINES
• Vertical lines go up and down.
• The x-value stays the same but the y-value changes.
• Vertical lines have the equation x = point equation crosses x-axis
• The slope of all vertical lines is undefined.
• Why is the slope undefined?
• Suppose you have points (1, 5) and (1, 3). You know they are
vertical because they have the same x-coordinate.
• Substitute into the slope formula.
y2 − y1 5 − 3 2
m= = =
x2 − x1 1 − 1 0
• Can’t have division by 0. Therefore, the slope is undefined.

46. WRITE THE EQUATIONS
( 2, −5 )

47. WRITE THE EQUATIONS
( 2, −5 )
• Write the equation for the vertical line that goes through the above
point.

48. WRITE THE EQUATIONS
( 2, −5 )
• Write the equation for the vertical line that goes through the above
point.
• Because the x-coordinate never changes, the equation is x = 2.

49. WRITE THE EQUATIONS
( 2, −5 )
• Write the equation for the vertical line that goes through the above
point.
• Because the x-coordinate never changes, the equation is x = 2.
• Writethe equation for the horizontal line that goes through the
above point.

50. WRITE THE EQUATIONS
( 2, −5 )
• Write the equation for the vertical line that goes through the above
point.
• Because the x-coordinate never changes, the equation is x = 2.
• Writethe equation for the horizontal line that goes through the
above point.
• Because the y-coordinate never changes, the equation is y = -5.

51. YOU TRY...
( −7, 9 )

52. YOU TRY...
( −7, 9 )
• Write the equation for the vertical line that goes through the above
point.

53. YOU TRY...
( −7, 9 )
• Write the equation for the vertical line that goes through the above
point.
• Because the x-coordinate never changes, the equation is x = -7.

54. YOU TRY...
( −7, 9 )
• Write the equation for the vertical line that goes through the above
point.
• Because the x-coordinate never changes, the equation is x = -7.
• Writethe equation for the horizontal line that goes through the
above point.

55. YOU TRY...
( −7, 9 )
• Write the equation for the vertical line that goes through the above
point.
• Because the x-coordinate never changes, the equation is x = -7.
• Writethe equation for the horizontal line that goes through the
above point.
• Because the y-coordinate never changes, the equation is y = 9.

56. STANDARD FORM

57. STANDARD FORM
• An equation written in the form Ax + By = C

58. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form:

59. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form:
• A, B, and C must be Integers.

60. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form:
• A, B, and C must be Integers.
•A must be positive.

61. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form:
• A, B, and C must be Integers.
•A must be positive.
• Either A OR B can be 0. Both can NOT be 0.

62. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form:
• A, B, and C must be Integers.
•A must be positive.
• Either A OR B can be 0. Both can NOT be 0.
• As long as A ≠ 0, Ax must be the first term.

63. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form: Examples
• A, B, and C must be Integers. 2x − y = 5
•A must be positive.
5y = −3
• Either A OR B can be 0. Both can NOT be 0.
x + 2y = 4
• As long as A ≠ 0, Ax must be the first term.

64. STANDARD FORM
• An equation written in the form Ax + By = C
• Rules for standard form: Examples
• A, B, and C must be Integers. 2x − y = 5
•A must be positive.
5y = −3
• Either A OR B can be 0. Both can NOT be 0.
x + 2y = 4
• As long as A ≠ 0, Ax must be the first term.
Non Examples
−2x + y = 5 4
2x + 3y =
0.5y = −3.4 7

65. WRITING AN EQUATION IN STANDARD FORM
Write the equation
2
y − 1 = ( x + 3)
3
in standard form.

66. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3)
3
in standard form.

67. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3)
3
in standard form.
2 2
y −1= x + ⋅3
3 3

68. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form.
2 2
y −1= x + ⋅3
3 3

69. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form.
2 2
y −1= x + ⋅3
3 3
2
y −1= x + 2
3

70. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2
y −1= x + 2
3

71. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2
y −1= x + 2
+1 3 +1

72. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2
y −1= x + 2
+1 3 +1
2 2
− x − x
3 3

73. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2
y −1= x + 2
+1 3 +1
2 2
− x − x
3 3
2
− x+y=3
3

74. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2 • Multiplyby -3 so A is positive and
y −1= x + 2 no fractions exist.
+1 3 +1
2 2
− x − x
3 3
2
− x+y=3
3

75. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2 • Multiplyby -3 so A is positive and
y −1= x + 2 no fractions exist.
+1 3 +1
2 2 ⎛ 2 ⎞
− x − x −3 ⎜ − x ⎟ + −3 ⋅ y = −3 ⋅ 3
3 3 ⎝ 3 ⎠
2
− x+y=3
3

76. WRITING AN EQUATION IN STANDARD FORM
Write the equation • Distribute first.
2
y − 1 = ( x + 3) • Simplify multiplication.
3
in standard form. • Use the properties of equality to get
2 2 the constants on the right and the
y −1= x + ⋅3 variables on the left.
3 3
2 • Multiplyby -3 so A is positive and
y −1= x + 2 no fractions exist.
+1 3 +1
2 2 ⎛ 2 ⎞
− x − x −3 ⎜ − x ⎟ + −3 ⋅ y = −3 ⋅ 3
3 3 ⎝ 3 ⎠
2
− x+y=3 2x − 3y = −9
3

77. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.

78. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.
• Symbol used to represent: ∕∕

79. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.
• Symbol used to represent: ∕∕
• Real life examples...

80. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.
• Symbol used to represent: ∕∕
• Real life examples...
• The top of the Berlin Wall and ground in
Berlin, Germany.

81. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.
• Symbol used to represent: ∕∕
• Real life examples...
• The top of the Berlin Wall and ground in
Berlin, Germany.

82. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.
• Symbol used to represent: ∕∕
• Real life examples...
• The top of the Berlin Wall and ground in
Berlin, Germany.
• The towers of the Tower Bridge in
London, England.

83. PARALLEL
• Parallel lines are 2 lines that never
touch. The distance between them remains
constant forever.
• Symbol used to represent: ∕∕
• Real life examples...
• The top of the Berlin Wall and ground in
Berlin, Germany.
• The towers of the Tower Bridge in
London, England.

84. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.

85. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.
• Symbol used to represent: ⊥

86. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.
• Symbol used to represent: ⊥
• Real life examples...

87. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.
• Symbol used to represent: ⊥
• Real life examples...
• The adjacent sides of a picture
frame located in the Louvre
Museum in Paris, France.

88. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.
• Symbol used to represent: ⊥
• Real life examples...
• The adjacent sides of a picture
frame located in the Louvre
Museum in Paris, France.

89. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.
• Symbol used to represent: ⊥
• Real life examples...
• The adjacent sides of a picture
frame located in the Louvre
Museum in Paris, France.
• The frame of a doorway in the
ruins of Pompeii, Italy.

90. PERPENDICULAR
• Perpendicular lines are 2 lines
that intersect at a 90 degree angle.
• Symbol used to represent: ⊥
• Real life examples...
• The adjacent sides of a picture
frame located in the Louvre
Museum in Paris, France.
• The frame of a doorway in the
ruins of Pompeii, Italy.

91. EXPLORATION ON GRAPHING CALCULATOR

92. EXPLORATION ON GRAPHING CALCULATOR
• Parallel lines and Perpendicular lines can be VERY
deceiving on a graphing calculator.

93. EXPLORATION ON GRAPHING CALCULATOR
• Parallel lines and Perpendicular lines can be VERY
deceiving on a graphing calculator.
• Enter
these 2 equations in y= and graph on a standard window
(Zoom - 6:ZStandard)
• y1 = .1x - 3
• y2 = .11x + 3

94. EXPLORATION ON GRAPHING CALCULATOR
• Parallel lines and Perpendicular lines can be VERY
deceiving on a graphing calculator.
• Enter
these 2 equations in y= and graph on a standard window
(Zoom - 6:ZStandard)
• y1 = .1x - 3
• y2 = .11x + 3
• Are these parallel, perpendicular or neither based on the screen?

95. EXPLORATION ON GRAPHING CALCULATOR
• Parallel lines and Perpendicular lines can be VERY
deceiving on a graphing calculator.
• Enter
these 2 equations in y= and graph on a standard window
(Zoom - 6:ZStandard)
• y1 = .1x - 3
• y2 = .11x + 3
• Are these parallel, perpendicular or neither based on the screen?
• Do the same with these equations.
• y1 = 1.9x - 3
• y2 = -1.2x - 3

96. EXPLORATION ON GRAPHING CALCULATOR
• Parallel lines and Perpendicular lines can be VERY
deceiving on a graphing calculator.
• Enter
these 2 equations in y= and graph on a standard window
(Zoom - 6:ZStandard)
• y1 = .1x - 3
• y2 = .11x + 3
• Are these parallel, perpendicular or neither based on the screen?
• Do the same with these equations.
• y1 = 1.9x - 3
• y2 = -1.2x - 3
• Keep your answers because you will need them shortly!

97. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.

98. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.

99. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.
• Same slope, different y-intercept = parallel lines

100. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.
• Same slope, different y-intercept = parallel lines
Parallel
y = 2x − 5
y = 2x + 5

101. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.
• Same slope, different y-intercept = parallel lines
• Same slope, same y-intercept = SAME line
Parallel
y = 2x − 5
y = 2x + 5

102. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.
• Same slope, different y-intercept = parallel lines
• Same slope, same y-intercept = SAME line
Same line
Parallel (÷ second by 5)
y = 2x − 5 y = −x + 3
y = 2x + 5 5y = −5x + 15

103. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.
• Same slope, different y-intercept = parallel lines
• Same slope, same y-intercept = SAME line
• Different slope, same or different y-intercept = intersecting lines
Same line
Parallel (÷ second by 5)
y = 2x − 5 y = −x + 3
y = 2x + 5 5y = −5x + 15

104. PARALLEL LINES
• Becausethe distance never changes between parallel lines, their
slopes must remain constant or eventually they will cross.
• To determine if 2 lines are parallel, check the slope.
• Same slope, different y-intercept = parallel lines
• Same slope, same y-intercept = SAME line
• Different slope, same or different y-intercept = intersecting lines
Same line
Parallel (÷ second by 5) NOT parallel
y = 2x − 5 y = −x + 3 y = 4x + 7
y = 2x + 5 5y = −5x + 15 y = 3x + 7

105. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
y2 = .11x + 3

106. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3

107. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3
• Why do you still agree or why did you change you mind?

108. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3
• Why do you still agree or why did you change you mind?
• These equations look parallel on the graphing calculator but what do
you notice about the slopes?

109. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3
• Why do you still agree or why did you change you mind?
• These equations look parallel on the graphing calculator but what do
you notice about the slopes?
• The slopes are different. They are very close, which is why they appear
parallel on the graphing calculator.

110. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3
• Why do you still agree or why did you change you mind?
• These equations look parallel on the graphing calculator but what do
you notice about the slopes?
• The slopes are different. They are very close, which is why they appear
parallel on the graphing calculator.
• Change your window settings to Xmin=-1100, Xmax=5, Ymin=-100,
Ymax=5 and graph the 2 equations again.

111. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3
• Why do you still agree or why did you change you mind?
• These equations look parallel on the graphing calculator but what do
you notice about the slopes?
• The slopes are different. They are very close, which is why they appear
parallel on the graphing calculator.
• Change your window settings to Xmin=-1100, Xmax=5, Ymin=-100,
Ymax=5 and graph the 2 equations again.
• Can you see the lines intersect now?

112. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel,
Perpendicular, or Neither? y1 = .1x −3
• Do you agree with your original answer?
y2 = .11x + 3
• Why do you still agree or why did you change you mind?
• These equations look parallel on the graphing calculator but what do
you notice about the slopes?
• The slopes are different. They are very close, which is why they appear
parallel on the graphing calculator.
• Change your window settings to Xmin=-1100, Xmax=5, Ymin=-100,
Ymax=5 and graph the 2 equations again.
• Can you see the lines intersect now?
• The Window setting is crucial to “seeing” if the equations are parallel. It is
easier to determine parallel lines by comparing the slopes.

113. PERPENDICULAR LINES
• Stand up nice and tall. What do you notice about your body in
relation to the floor? Are you parallel or perpendicular with the floor?

114. PERPENDICULAR LINES
• Stand up nice and tall. What do you notice about your body in
relation to the floor? Are you parallel or perpendicular with the floor?
• Foryou to be parallel, you must lay your body on the floor. (This
change is called a “rotation” in math.) Standing you meet the floor at
a 90 degree angle so the “rotation” would be 90 degrees for you to
be parallel to the floor.

115. PERPENDICULAR LINES
• Stand up nice and tall. What do you notice about your body in
relation to the floor? Are you parallel or perpendicular with the floor?
• Foryou to be parallel, you must lay your body on the floor. (This
change is called a “rotation” in math.) Standing you meet the floor at
a 90 degree angle so the “rotation” would be 90 degrees for you to
be parallel to the floor.
• Draw a coordinate plane on your paper. Place 2 pencils on the graph
so they cross with a 90 degree angle. Don’t place them vertical and
horizontal on the coordinate plane because these are a special case
but do move them around maintaining the 90 degree angle.

116. PERPENDICULAR LINES
• Stand up nice and tall. What do you notice about your body in
relation to the floor? Are you parallel or perpendicular with the floor?
• Foryou to be parallel, you must lay your body on the floor. (This
change is called a “rotation” in math.) Standing you meet the floor at
a 90 degree angle so the “rotation” would be 90 degrees for you to
be parallel to the floor.
• Draw a coordinate plane on your paper. Place 2 pencils on the graph
so they cross with a 90 degree angle. Don’t place them vertical and
horizontal on the coordinate plane because these are a special case
but do move them around maintaining the 90 degree angle.
• What did you notice about the slopes of the pencils? Both positive?
Both negative? One of each? ...

117. PERPENDICULAR LINES (CONTINUED)
• Noticeone is always positive and one is
always negative.

118. PERPENDICULAR LINES (CONTINUED)
• Noticeone is always positive and one is
always negative.
• Perpendicular
lines have slopes that are
negative reciprocals.

119. PERPENDICULAR LINES (CONTINUED)
• Noticeone is always positive and one is
always negative.
• Perpendicular
lines have slopes that are
negative reciprocals.
• Negative reciprocals mean the slopes
have opposite signs and the number is flipped.

120. PERPENDICULAR LINES (CONTINUED)
• Noticeone is always positive and one is
always negative.
Perpendicular
y = 2x − 3
• Perpendicular
lines have slopes that are
negative reciprocals. 1
y=− x+5
• Negative reciprocals mean the slopes 2
have opposite signs and the number is flipped.
• Such as -1/2 and 2 are negative reciprocals.

121. PERPENDICULAR LINES (CONTINUED)
• Noticeone is always positive and one is
always negative.
Perpendicular
y = 2x − 3
• Perpendicular
lines have slopes that are
negative reciprocals. 1
y=− x+5
• Negative reciprocals mean the slopes 2
have opposite signs and the number is flipped.
• Such as -1/2 and 2 are negative reciprocals.
•3 and -3 are opposite
but NOT reciprocals. NOT ⊥
y = 3x + 7
y = −3x + 7

122. PERPENDICULAR LINES (CONTINUED)
• Noticeone is always positive and one is
always negative.
Perpendicular
y = 2x − 3
• Perpendicular
lines have slopes that are
negative reciprocals. 1
y=− x+5
• Negative reciprocals mean the slopes 2
have opposite signs and the number is flipped.
• Such as -1/2 and 2 are negative reciprocals.
Perpendicular
•3 and -3 are opposite 3
but NOT reciprocals. NOT ⊥ y = x −1
4
• 3/4and -4/3 are negative y = 3x + 7
reciprocals. Can have 4
y = −3x + 7 y = − x −1
the same y-intercept. 3

123. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
y2 = −1.2x − 3

124. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3

125. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3
• Why do you still agree or why did you change you mind?

126. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3
• Why do you still agree or why did you change you mind?
• These equations look perpendicular on the graphing calculator but what do you
notice about the slopes?

127. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3
• Why do you still agree or why did you change you mind?
• These equations look perpendicular on the graphing calculator but what do you
notice about the slopes?
• The slopes are NOT negative reciprocals! (1.9 = 19/10 and -1.2 = -6/5) They
are very close, which is why they appear perpendicular on the graphing calculator.

128. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3
• Why do you still agree or why did you change you mind?
• These equations look perpendicular on the graphing calculator but what do you
notice about the slopes?
• The slopes are NOT negative reciprocals! (1.9 = 19/10 and -1.2 = -6/5) They
are very close, which is why they appear perpendicular on the graphing calculator.
• Change your window settings to Xmin=-5, Xmax=5 and graph the 2 equations
again.

129. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3
• Why do you still agree or why did you change you mind?
• These equations look perpendicular on the graphing calculator but what do you
notice about the slopes?
• The slopes are NOT negative reciprocals! (1.9 = 19/10 and -1.2 = -6/5) They
are very close, which is why they appear perpendicular on the graphing calculator.
• Change your window settings to Xmin=-5, Xmax=5 and graph the 2 equations
again.
• Do they appear perpendicular?

130. BACK TO THE EXPLORATION
• What did you say about the graph of these equations? Parallel, Perpendicular, or
Neither?
y1 = 1.9x − 3
• Do you agree with your answer? You may want to change
these to fractions to make a better determination. y2 = −1.2x − 3
• Why do you still agree or why did you change you mind?
• These equations look perpendicular on the graphing calculator but what do you
notice about the slopes?
• The slopes are NOT negative reciprocals! (1.9 = 19/10 and -1.2 = -6/5) They
are very close, which is why they appear perpendicular on the graphing calculator.
• Change your window settings to Xmin=-5, Xmax=5 and graph the 2 equations
again.
• Do they appear perpendicular?
• Like for parallel lines, the Window setting is crucial to “seeing” if the equations are
perpendicular. It is easier to determine perpendicular lines by comparing the slopes.

131. FINDING ∕∕ OR ⊥ SLOPE
2x − y = 5

132. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
before determining the slope of
the given line.

133. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.

134. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5

135. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
−1 −1

136. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
−1 −1
y = 2x − 5

137. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
• Identify the slope.
−1 −1
y = 2x − 5

138. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
• Identify the slope.
−1 −1
y = 2x − 5
m=2

139. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
• Identify the slope.
−1 −1
• Parallel slopes are the same.
y = 2x − 5
m=2

140. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
• Identify the slope.
−1 −1
• Parallel slopes are the same.
y = 2x − 5
m=2
Parallel slope
m=2

141. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
• Identify the slope.
−1 −1
• Parallel slopes are the same.
y = 2x − 5
m=2 • Perpendicular slopes are negative
reciprocals.
Parallel slope
m=2

142. FINDING ∕∕ OR ⊥ SLOPE
• Always put equation in slope-
2x − y = 5 intercept form (y = mx + b)
−2x −2x before determining the slope of
the given line.
−y = −2x + 5
• Identify the slope.
−1 −1
• Parallel slopes are the same.
y = 2x − 5
m=2 • Perpendicular slopes are negative
reciprocals.
Perpendicular slope
Parallel slope
1
m=2 m=−
2

143. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7

144. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
before determining the slope of
the given line.

145. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.

146. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7

147. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7
2 2

148. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7
2 2
3 7
y= x+
2 2

149. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7
2 2 • Identify the slope.
3 7
y= x+
2 2

150. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7
2 2 • Identify the slope.
3 7
y= x+
2 2
3
m=
2

151. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7
2 2 • Identify the slope.
3 7 • Parallel slopes are the same.
y= x+
2 2
3
m=
2
Parallel slope
3
m=
2

152. YOUR TURN TO FIND ∕∕ & ⊥ SLOPE...
−3x + 2y = 7 • Always put equation in slope-
intercept form (y = mx + b)
+3x +3x before determining the slope of
the given line.
2y = 3x + 7
2 2 • Identify the slope.
3 7 • Parallel slopes are the same.
y= x+
2 2
• Perpendicular slopes are negative
3
m= reciprocals.
2
Perpendicular slope
Parallel slope
3
2
m= m=−
2 3

153. WRITING ∕∕ EQUATION
Write the slope-intercept form of the
equation parallel to y = -3x + 4,
which passes through the point (2, -5).

154. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)

155. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3

156. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.

157. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
• Use point-slope formula to find parallel
equation.

158. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
equation.

159. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
equation.
• Substitute given point and parallel slope.

160. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − ( −5 ) = −3( x − 2 ) equation.
• Substitute given point and parallel slope.

161. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − ( −5 ) = −3( x − 2 ) equation.
• Substitute given point and parallel slope.
• Put equation in slope-intercept form.

162. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − ( −5 ) = −3( x − 2 ) equation.
y + 5 = −3x + 6 • Substitute given point and parallel slope.
• Put equation in slope-intercept form.

163. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − ( −5 ) = −3( x − 2 ) equation.
y + 5 = −3x + 6 • Substitute given point and parallel slope.
−5 −5
• Put equation in slope-intercept form.

164. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − ( −5 ) = −3( x − 2 ) equation.
y + 5 = −3x + 6 • Substitute given point and parallel slope.
−5 −5
• Put equation in slope-intercept form.
y = −3x + 1

165. WRITING ∕∕ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation parallel to y = -3x + 4, equation. (May need to put in slope-
which passes through the point (2, -5). intercept form.)
m = −3 • Parallel slopes are the same so use m =
-3.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − ( −5 ) = −3( x − 2 ) equation.
y + 5 = −3x + 6 • Substitute given point and parallel slope.
−5 −5
• Put equation in slope-intercept form.
• Always check your equation to ensure it
y = −3x + 1 makes sense. The lines are parallel so
the slopes must be the same (they are)
and y-intercepts different (they are).

166. YOUR TURN...
Write the slope-intercept form of the
equation parallel to y = 4x + 7, which
passes through the point (-3, 8).

167. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)

168. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4

169. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.

170. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
• Use point-slope formula to find parallel
equation.

171. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
equation.

172. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
equation.
• Substitute given point and parallel slope.

173. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
• Substitute given point and parallel slope.

174. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
• Substitute given point and parallel slope.
• Put equation in slope-intercept form.

175. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
y − 8 = 4 ( x + 3) • Substitute given point and parallel slope.
• Put equation in slope-intercept form.

176. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
y − 8 = 4 ( x + 3) • Substitute given point and parallel slope.
y − 8 = 4x + 12 • Put equation in slope-intercept form.

177. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
y − 8 = 4 ( x + 3) • Substitute given point and parallel slope.
y − 8 = 4x + 12 • Put equation in slope-intercept form.
+8 +8

178. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
y − 8 = 4 ( x + 3) • Substitute given point and parallel slope.
y − 8 = 4x + 12 • Put equation in slope-intercept form.
+8 +8
y = 4x + 20

179. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation parallel to y = 4x + 7, which equation. (No need to put in slope-
passes through the point (-3, 8). intercept form here.)
m=4 • Parallel slopes are the same so use m =
4.
y − y1 = m ( x − x1 )
• Use point-slope formula to find parallel
y − 8 = 4 ( x − ( −3)) equation.
y − 8 = 4 ( x + 3) • Substitute given point and parallel slope.
y − 8 = 4x + 12 • Put equation in slope-intercept form.
+8 +8 • Check that equation makes sense. The
lines are parallel so the slopes must be
the same (they are) and y-intercepts
y = 4x + 20 different (they are).

180. WRITING ⊥ EQUATION
Write the slope-intercept form of the
equation perpendicular to y = -5x + 2,
which passes through the point (10, 3).

181. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)

182. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5

183. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 • Perpendicular slopes are negative
reciprocals.

184. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.

185. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
• Use point-slope formula to find
perpendicular equation.

186. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
perpendicular equation.

187. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
perpendicular equation.
• Substitute given point and perpendicular
slope.

188. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
1 perpendicular equation.
y − 3 = ( x − 10 )
5 • Substitute given point and perpendicular
slope.

189. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
1 perpendicular equation.
y − 3 = ( x − 10 )
5 • Substitute given point and perpendicular
slope.
• Put equation in slope-intercept form.

190. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
1 perpendicular equation.
y − 3 = ( x − 10 )
5 • Substitute given point and perpendicular
1 slope.
y−3= x−2
5 • Put equation in slope-intercept form.

191. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
1 perpendicular equation.
y − 3 = ( x − 10 )
5 • Substitute given point and perpendicular
1 slope.
y−3= x−2
+3 5 +3 • Put equation in slope-intercept form.

192. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
1 perpendicular equation.
y − 3 = ( x − 10 )
5 • Substitute given point and perpendicular
1 slope.
y−3= x−2
+3 5 +3 • Put equation in slope-intercept form.
1
y = x +1
5

193. WRITING ⊥ EQUATION
Write the slope-intercept form of the • Always determine the slope of the given
equation perpendicular to y = -5x + 2, equation. (May need to put in slope-
which passes through the point (10, 3). intercept form.)
m = −5 1 • Perpendicular slopes are negative
m⊥ =
5 reciprocals.
y − y1 = m ( x − x1 ) • Use point-slope formula to find
1 perpendicular equation.
y − 3 = ( x − 10 )
5 • Substitute given point and perpendicular
1 slope.
y−3= x−2
+3 5 +3 • Put equation in slope-intercept form.
• Always check your equation to ensure it
1 makes sense. The lines are perpendicular
y = x +1 so the slopes must be negative
5 reciprocals (they are).

194. YOUR TURN...
Write the slope-intercept form of the
equation perpendicular to y = 3x - 1,
which passes through the point (6, 9).

195. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)

196. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3

197. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 • Perpendicular slopes are negative
reciprocals.

198. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.

199. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
• Use point-slope formula to find
perpendicular equation.

200. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
perpendicular equation.

201. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
perpendicular equation.
• Substitute given point and
perpendicular slope.

202. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
1 perpendicular equation.
y − 9 = − ( x − 6)
3 • Substitute given point and
perpendicular slope.

203. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
1 perpendicular equation.
y − 9 = − ( x − 6)
3 • Substitute given point and
perpendicular slope.
• Put equation in slope-intercept form.

204. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
1 perpendicular equation.
y − 9 = − ( x − 6)
3 • Substitute given point and
1 perpendicular slope.
y−3= − x+2
3 • Put equation in slope-intercept form.

205. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
1 perpendicular equation.
y − 9 = − ( x − 6)
3 • Substitute given point and
1 perpendicular slope.
y−3= − x+2
+3 3 +3 • Put equation in slope-intercept form.

206. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
1 perpendicular equation.
y − 9 = − ( x − 6)
3 • Substitute given point and
1 perpendicular slope.
y−3= − x+2
+3 3 +3 • Put equation in slope-intercept form.
1
y=− x+5
3

207. YOUR TURN...
Write the slope-intercept form of the • Determine the slope of the given
equation perpendicular to y = 3x - 1, equation. (No need to put in slope-
which passes through the point (6, 9). intercept form here.)
m=3 1
m⊥ = − • Perpendicular slopes are negative
3 reciprocals.
y − y1 = m ( x − x1 )
• Use point-slope formula to find
1 perpendicular equation.
y − 9 = − ( x − 6)
3 • Substitute given point and
1 perpendicular slope.
y−3= − x+2
+3 3 +3 • Put equation in slope-intercept form.
1 • Check that equation makes sense. The
y=− x+5 lines are perpendicular so the slopes
must be negative reciprocals (they are).
3