Rate of Change

1. Section 2.3
Rate of Change & Slope of a Line
 Average Rate of Change
 Slope of a Line
 Applications
 Horizontal & Vertical Lines
 Slopes of Parallel Line
 Slopes of Perpendicular Lines

2. Slope is a Ratio:
Average Rate of Change Examples

3. What is Slope & Why is it Important?
 Using any 2 points on a straight line will
compute to the same slope.
 We use the letter m to stand for a line’s slope

4. Examples
 Compute the slope of a
line passing through
(-2,4) and (3,-4)
8
5
4  ( 
4)
 
2 (3)


m 
 Find the slope of
8
5
 
the line on this graph:

5. Class Exercise:
Compute the slope for each pair of points
 (0,-3) and (-3,2)
 (-2,7) and (3,5)
 (0,0) and (60,80)
 (4,0) and (7,0)
5
3
5
3
 

3 2
0 3
 
3 2
0 3
 



 
2
5
2
5
7 
5
2 3
 


 
4
3
80
60
0 
80
0 60





0
0
3
0 
0
4 7





6. Class Exercise:
 Example 3: Building Stairs p.125

7. Horizontal Line Equations – 0 Slope

8. Vertical Line Equations – Undefined Slope

9. Examples of Vertical Lines
Find the slope of
2y = 10

10. Parallel Lines
(Two Lines on the Same Graph with Same Slope)

11. Slopes of Parallel Lines
m1 = m2
One line has a slope of -1/3. A different line
passes through the points (-6,2) and (3,-1). Are
the lines parallel?
Compute the slope of the second line:
[2 - -1]/[-6 – 3] = [3]/[-9] = -1/3
(They are Parallel)

12. Slopes of Perpendicular Lines
m1 = -1 / m2

13. Slopes of Perpendicular Lines
m1 = -1 / m2

14. The Dope on Slope
 On a graph, the average rate of change is the ratio of the change
in y to the change in x
 For straight lines, the slope is the rate of change between any 2
different points
 The letter m is used to signify a line’s slope
If there are two lines, we use m1 and m2
 The slope of a line passing through the two points (x1,y1) and
(x2,y2) can be computed m=(y2–y1)/(x2–x1)
 Horizontal lines (like y=3) have slope 0
 Vertical lines (like x=-5) have an undefined slope
 Parallel lines have the same slope m1 = m2
 Perpendicular lines have negative reciprocal slopes m1=-1/m2

15. What Next?
 Present Section 2.4
Writing Equations of Lines