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SLOPES AND
EQUATIONS OF LINES
SLOPE
Slope is the rate of change of a straight line (linear)
graph/function.
 What are some of the things we have learne...
SLOPE CONT.
 Positive slopes mean the graph is going up from left to
right
 Negative slopes mean the graph is going down...
HOW TO CALCULATE SLOPE…
To calculate a slope from a graph or two
coordinate points we use the formula:

Image From: http:...
FINDING SLOPE
• Use the slope formula to find the slope of the
given examples.
1. (-2, 5) and (4, 12)
2.

Image From: http...
SLOPE VIDEOS
Graphical Example for Slope of a
Line

Example of Finding Slope given Two Points

Video From: Khan Academy
LINEAR FUNCTIONS
Linear Functions are functions whose
graphs are straight lines. They are
straight because their rate (slo...
SLOPE-INTERCEPT FORM

 It is slope-intercept form because the y (or dependent variable) is by
itself and the highest expo...
EXAMPLES
Write the equation of the line in slope-intercept form.
1.

2.

3. m= 1/5
b = -2

4. y-intercept = 200
slope = -2...
SPECIAL CASES
 Horizontal Lines have a slope of 0. Therefore, we cannot
write a slope-intercept equation for them.
Horiz...
SLOPE-INTERCEPT VIDEO

Slope-Intercept
Equation

Video From: Khan Academy
LINEAR STANDARD FORM
This is another form for writing a linear
function.
It is used to represent situations where two
va...
WHICH EQUATIONS ARE IN LINEAR STANDARD FORM?
Linear Standard
Form

-2x – 4y = 9
X=2
Y=1

Not Linear Standard
Form

1/3x – ...
STANDARD FORM VIDEOS

Standard Form
Equations

Video From: Khan Academy
POINT-SLOPE FORM
• We use point-slope form when we have a point and
a slope of a line

Image From:
POINT-SLOPE VIDEO
Ideas Behind Point-Slope
Form
Point-Slope Form
Examples
WRITE A POINT-SLOPE EQUATION
1. (2, 5) and m = ½

1. (-8, 12) and slope = -3

1. (-6, 0) and m = 8

1. Point: (-1, -6) and...
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Slope and Equations of Lines

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Transcript of "Slope and Equations of Lines"

  1. 1. SLOPES AND EQUATIONS OF LINES
  2. 2. SLOPE Slope is the rate of change of a straight line (linear) graph/function.  What are some of the things we have learned about slope so far?  Can you come up with an equation to calculate slope? Image From: http://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-
  3. 3. SLOPE CONT.  Positive slopes mean the graph is going up from left to right  Negative slopes mean the graph is going down from left to right  The steeper the line the bigger the slope (rate of change) Image From: http://www.sparknotes.com/math/algebra1/writingequations/section1.rhtml Image From:
  4. 4. HOW TO CALCULATE SLOPE… To calculate a slope from a graph or two coordinate points we use the formula: Image From: http://math.about.com/od/allaboutslope/ss/Find-Slope-With-Formula-
  5. 5. FINDING SLOPE • Use the slope formula to find the slope of the given examples. 1. (-2, 5) and (4, 12) 2. Image From: https://www.mathscore.com/math/skills/DetSlope.html
  6. 6. SLOPE VIDEOS Graphical Example for Slope of a Line Example of Finding Slope given Two Points Video From: Khan Academy
  7. 7. LINEAR FUNCTIONS Linear Functions are functions whose graphs are straight lines. They are straight because their rate (slope) is constant. There are 3 forms of a linear function. • Slope-Intercept Form • Standard Form • Point-Slope Form
  8. 8. SLOPE-INTERCEPT FORM  It is slope-intercept form because the y (or dependent variable) is by itself and the highest exponent of x (or independent variable) is 1.  The slope is always the value with the x in THIS FORM. It could be written y = b + mx. Image From: http://bronxarena.org/mobile/courses/algebrab/challenge1/1.5.html
  9. 9. EXAMPLES Write the equation of the line in slope-intercept form. 1. 2. 3. m= 1/5 b = -2 4. y-intercept = 200 slope = -23.724 Image From: http://hotmath.com/help/gt/genericalg1/section_9_2.html Image From: http://www.mathsteacher.com.au/year8/ch15_graphs/04_plot/graphs.htm
  10. 10. SPECIAL CASES  Horizontal Lines have a slope of 0. Therefore, we cannot write a slope-intercept equation for them. Horizontal lines intersect the y-axis. Therefore, the equation for a horizontal line just states what that y-value is.  Vertical lines have an undefined slope. Therefore, we cannot write a slope-intercept equation for them, either. • Instead, we notice that the coordinate points of a vertical all have the same x-value. • So, the equation for a vertical line just states what that x-value is.
  11. 11. SLOPE-INTERCEPT VIDEO Slope-Intercept Equation Video From: Khan Academy
  12. 12. LINEAR STANDARD FORM This is another form for writing a linear function. It is used to represent situations where two variables are changing at a constant rate. In this form, the A, B, and C do not represent the y-intercept or the slope of the graph. It is also important to understand that in many cases standard form is only written using integers (+/- whole numbers) for A, B, and C. It is possible for A, B, and C to be zero but it cannot be both A and B.
  13. 13. WHICH EQUATIONS ARE IN LINEAR STANDARD FORM? Linear Standard Form -2x – 4y = 9 X=2 Y=1 Not Linear Standard Form 1/3x – 7y = 12 y = -1/2x + 3 y – 4 = 2(x + 5) 8 = 2.5x – 3y 10 = -3xy 4x + 3y = 20
  14. 14. STANDARD FORM VIDEOS Standard Form Equations Video From: Khan Academy
  15. 15. POINT-SLOPE FORM • We use point-slope form when we have a point and a slope of a line Image From:
  16. 16. POINT-SLOPE VIDEO Ideas Behind Point-Slope Form Point-Slope Form Examples
  17. 17. WRITE A POINT-SLOPE EQUATION 1. (2, 5) and m = ½ 1. (-8, 12) and slope = -3 1. (-6, 0) and m = 8 1. Point: (-1, -6) and Point: (-3, 4) 5.
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