Rate of Change

1
Rate of Change

• Rate of change vertical change (y)
  difference in y
• horizontal change (x) difference in x

2
Finding Rate of Change Using a Table
ALGEBRA 1 LESSON 6-1
Find the rate of change for each pair of
consecutive mileage amounts.
6-1
3
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
(continued)
The rate of change for each pair of consecutive
mileage amounts is 12 per 50 miles. The rate of
change is the same for all the data.
6-1
4
Number of Days Rental Charge
1 60
2 75
3 90
4 105
5 120
5
Finding Rate of Change Using a Graph
ALGEBRA 1 LESSON 6-1
6-1
6
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
(continued)
Using the points (0,0) and (20, 400), find the
rate of change.
The rate of change is 20 m/s. The motorcycle is
traveling 20 meters each second.
6-1
7
You Try

• In your book, turn to page 283. Look at Example
  2, number 2
• Find the rate of change of the data in the graph.
  Explain what this rate of change means.

8
Finding Slope

• Slope vertical change rise
  difference in ys
• horizontal change run
  difference in xs

9
Finding Slope Using a Graph
ALGEBRA 1 LESSON 6-1
Find the slope of each line.
6-1
10
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
(continued)
The slope of the line is 2.
6-1
11
You try

• Turn to page 284, example 3 number 3.
• Find the slope of each line a and b.

12
Finding Slope Using Points

• Slope Formula rise y y , where x - x
  ? 0
• run x x

13
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
6-1
14
Horizontal and Vertical Lines
ALGEBRA 1 LESSON 6-1
The slope of the horizontal line is 0.
6-1
15
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
(continued)
Find the slope of the line.
b.
Division by zero is undefined. The slope of the
vertical line in undefined.
6-1
16
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
10. 2 11. 2 12. 13. 14. 1 15.
1 16. 17. 18. 19.
20. 21. 5 22. 0 23. undefined 24. 0 25.
undefined 26. 0 27. in./month 28.
5/person 29. 30 mi/hr 30.
1 2
Blue is Objective 1 Red is Objective 2 1.
3 the temperature increases 3F each hour. 2.
3.95 the cost per person is 3.95. 3.
gal/mi 4. there are 2 lb of carbon
emissions for 3 h of television use. 5. 16
the skydiver descends 16 ft/s. 6. the
cost of oregano is 1 for 4 ounces. 8. 3
3 4
1 15
3 2
2 3
2 3
2 3
5 9
1 4
5 3
6 5
1 2
2 5
6-1
17
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
41. a. b. c. Answers may vary.
Sample 42. 2 3 43. No for example
the line passing through the points such as (1,
6) and (2, 5) has a slope of 1. 44. PQ QR
0 RS 5 SP 1 45. JK KL 2 ML
MJ 2
38. 39. 40. a. C b. C greatest
A least the slope
31. 32. 33. 20 34. undefined 35.
3 36. 37.
2 3
1 6
2 3
1 4
2 5
3 5
6-1
18
Rate of Change and Slope
ALGEBRA 1 LESSON 6-1
6-1