Slope, Parallel and
Perpendicular Lines
.
Try these…..Review
1.Find the reciprocal of each fraction
a.

1
2

b.

4
3

c.

1
−
3

d.

5
−
2

2.Find the slope and y-i...
Quick Review/Preview
1. What is the Slope-Intercept Form?
y = mx + b
2. What is the Standard Form?
Ax + By = C
3. What is ...
Overview
How to calculate a slope
 Parallel Lines and Perpendicular Lines
 Write equations for each type of lines

Notes
Finding the Slope of a Line

Slope is found using the equation m= y2 -y1.
x2 -x1
The coordinates for the points on t...
Notes
Classifying Lines Using Slope





A line with a positive slope rises from left to right. (m>0)
A line with a ne...
Notes Continued

Slopes of Parallel and Perpendicular Lines
Parallel Lines The lines are parallel if and only if they have...
Parallel Lines
Parallel Lines - lines that never intersect
What is the slope of the
red line?
1/2
What is the slope of the...
Parallel Lines
Determine if the lines are parallel

1
1. 2 x + 6 y = 12 and y = − x + 5
3
2x + 6y = 12
6y = -2x + 12
1
y =...
Parallel Lines
Determine if the lines are parallel

3
2. 6 x + 8 y = −24 and y = x − 3
4
6x + 8y = -24
8y = -6x – 24
3
y =...
Parallel Lines
Determine if the lines are parallel

2
3. 4 x + 6 y = −2 and y = x −8
3
4x + 6y = -2
6y = -4x – 2
2
1
y = −...
Perpendicular Lines
Perpendicular Lines – lines that intersect to form
right angles
What is the slope of the
red line?
-1/...
Perpendicular Lines
What is the slope of the perpendicular line?

2
7. y = x − 8
5
1
8. y = − x
5
9. y = −2 x − 7

-5/2
5/...
Equations of Perpendicular Lines
10. Find the equation of the line that
contains (0, -2) and is perpendicular to
y = 5x + ...
Equations of Perpendicular Lines
11. Find the equation of the line that
contains (1, 8) and is perpendicular to

3
y = x+1...
Equations of Perpendicular Lines
12. Find the equation of the line that
contains (2, -3) and is perpendicular to

1
y = − ...
Perpendicular Lines
13. Determine if the lines are perpendicular:
2
y = x + 1 and 3 y + 2 x = 4
3

3y + 2x = 4

3 y = −2 x...
Challenge
What is the slope of the line that is parallel
to x = 4?
undefined
 What is the slope of the line that is
perpe...
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Parallel and Perpendicular Slopes lines

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Parallel and Perpendicular Slopes lines

  1. 1. Slope, Parallel and Perpendicular Lines .
  2. 2. Try these…..Review 1.Find the reciprocal of each fraction a. 1 2 b. 4 3 c. 1 − 3 d. 5 − 2 2.Find the slope and y-intercept of each equation 5 a. y = x + 4 4 5 b. y = x − 8 3 c. y = 6 x d. y = 6 x + 2
  3. 3. Quick Review/Preview 1. What is the Slope-Intercept Form? y = mx + b 2. What is the Standard Form? Ax + By = C 3. What is the Point-Slope Form? y – y1 = m(x – x1) 4. Find the “negative reciprocal” of each fraction 2 3 7 1 2 4 3 5 a. b. − c. − − = 2 d. − 5 7 3 2 1 3 4 2
  4. 4. Overview How to calculate a slope  Parallel Lines and Perpendicular Lines  Write equations for each type of lines 
  5. 5. Notes Finding the Slope of a Line Slope is found using the equation m= y2 -y1. x2 -x1 The coordinates for the points on the graph are plugged into the equation above. The equation is then solved and the remaining solution is the slope. Example: Let (x1, y1) = (-3, 5) and (x2, y2) = (2, 1)
  6. 6. Notes Classifying Lines Using Slope     A line with a positive slope rises from left to right. (m>0) A line with a negative slope falls from left to right. (m<0) A line with a slope of zero is horizontal. (m=0) A line with an undefined slope is vertical. (m is undefined.) Positive Slope Negative Slope Zero Slope Undefined Slope
  7. 7. Notes Continued Slopes of Parallel and Perpendicular Lines Parallel Lines The lines are parallel if and only if they have the same slope. m1 = m2 Perpendicular Lines The lines are perpendicular if and only if their slopes are negative reciprocals of each other m1 = - 1 or m1m2 = -1 m2 Parallel Lines Perpendicular Lines
  8. 8. Parallel Lines Parallel Lines - lines that never intersect What is the slope of the red line? 1/2 What is the slope of the blue line? 1/2 Parallel Lines have the same slope!
  9. 9. Parallel Lines Determine if the lines are parallel 1 1. 2 x + 6 y = 12 and y = − x + 5 3 2x + 6y = 12 6y = -2x + 12 1 y = − x+2 3 yes
  10. 10. Parallel Lines Determine if the lines are parallel 3 2. 6 x + 8 y = −24 and y = x − 3 4 6x + 8y = -24 8y = -6x – 24 3 y = − x +3 4 No
  11. 11. Parallel Lines Determine if the lines are parallel 2 3. 4 x + 6 y = −2 and y = x −8 3 4x + 6y = -2 6y = -4x – 2 2 1 y = − x− 3 3 No
  12. 12. Perpendicular Lines Perpendicular Lines – lines that intersect to form right angles What is the slope of the red line? -1/4 What is the slope of the blue line? 4/1 Perpendicular Lines have negative reciprocal slope!
  13. 13. Perpendicular Lines What is the slope of the perpendicular line? 2 7. y = x − 8 5 1 8. y = − x 5 9. y = −2 x − 7 -5/2 5/1 = 5 1/2
  14. 14. Equations of Perpendicular Lines 10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3 1 m=− 5 1 y+2=− x 5
  15. 15. Equations of Perpendicular Lines 11. Find the equation of the line that contains (1, 8) and is perpendicular to 3 y = x+1 4 4 m =− 3 4 y − 8 = − ( x − 1) 3
  16. 16. Equations of Perpendicular Lines 12. Find the equation of the line that contains (2, -3) and is perpendicular to 1 y = − x+ 6 2 m=2 y + 3 = 2(x – 2)
  17. 17. Perpendicular Lines 13. Determine if the lines are perpendicular: 2 y = x + 1 and 3 y + 2 x = 4 3 3y + 2x = 4 3 y = −2 x + 4 2 4 y =− x+ 3 3 No 14. Determine if the lines are perpendicular: 4 y = x − 5 and 4 y + 3 x = 9 3 4y + 3 x = 9 4 y = −3 x + 9 y =− 3 9 x+ 4 4 Yes
  18. 18. Challenge What is the slope of the line that is parallel to x = 4? undefined  What is the slope of the line that is perpendicular to x = 4? zero 
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