1. Five-Minute Check (over Lesson 1–2) Mathematical Practices Then/Now
New Vocabulary
Example 1: Real-World Example: Constant Rate of Change
Example 2: Real-World Example: Average Rate of Change
Key Concept: Slope of a Line
Example 3: Find Slope Using Coordinates
Example 4: Find Slope Using a Graph
Lesson Menu

2. State whether f(x) = 2 + x2 is linear.
A. yes
B. No, the variable has an exponent of 2.
5-Minute Check 1

3. State whether f(x) = 2 + x2 is linear.
A. yes
B. No, the variable has an exponent of 2.
5-Minute Check 1

4. State whether x – y = –6 is linear.
A. yes
B. No, none of the variables have exponents.
5-Minute Check 2

5. State whether x – y = –6 is linear.
A. yes
B. No, none of the variables have exponents.
5-Minute Check 2

6. Write the equation 2 – y = 10x in standard form.
A. –10x + y = 2
B. –10x – y = 2
C. 10x + y = 2
D. 10x + y – 2 = 0
5-Minute Check 3

7. Write the equation 2 – y = 10x in standard form.
A. –10x + y = 2
B. –10x – y = 2
C. 10x + y = 2
D. 10x + y – 2 = 0
5-Minute Check 3

8. A. B. C. D.
5-Minute Check 4

9. A. B. C. D.
5-Minute Check 4

10. During exercise a person’s maximum heart rate r in beats per minute is estimated by r = 220 – a, where a is the person’s age in years. What is the maximum heart rate for a 32-year-old while exercising?
A. 252 beats per min
B. 192 beats per min
C. 188 beats per min
D. 178 beats per min
5-Minute Check 5

11. During exercise a person’s maximum heart rate r in beats per minute is estimated by r = 220 – a, where a is the person’s age in years. What is the maximum heart rate for a 32-year-old while exercising?
A. 252 beats per min
B. 192 beats per min
C. 188 beats per min
D. 178 beats per min
5-Minute Check 5

12. The initial fee to join a gym is $200
The initial fee to join a gym is $200. It costs $55 per month to have a membership. Write a function for the total cost, C(x) of having a membership for x months. What is the cost of having a membership for 18 months?
A. C(x) = x; $11,018
B. C(x) = x; $1190
C. C(x) = 200x + 55; $3655
D. C(x) = x; $3655
5-Minute Check 6

13. The initial fee to join a gym is $200
The initial fee to join a gym is $200. It costs $55 per month to have a membership. Write a function for the total cost, C(x) of having a membership for x months. What is the cost of having a membership for 18 months?
A. C(x) = x; $11,018
B. C(x) = x; $1190
C. C(x) = 200x + 55; $3655
D. C(x) = x; $3655
5-Minute Check 6

14. Mathematical Practices
8 Look for and express regularity in repeated reasoning.
Content Standards
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. MP

15. You graphed linear relations.
Find rate of change.
Determine the slope of a line.
Then/Now

16. rate of change
slope
Vocabulary

17. Constant Rate of Change
COLLEGE ADMISSIONS In 2004, 56,878 students applied to UCLA. In 2006, 60,291 students applied. Find the rate of change in the number of students applying for admission from 2004 to 2006.
Example 1

18. Constant Rate of Change
Answer:
Example 1

19. Constant Rate of Change
Answer: The rate of change is This means that the number of students applying for admission increased by each year.
Example 1

20. Find the rate of change for the data in the table.
A. 2 ft/min
B. 3 ft/min
C. 4 ft/min
D. 6 ft/min
Example 1

21. Find the rate of change for the data in the table.
A. 2 ft/min
B. 3 ft/min
C. 4 ft/min
D. 6 ft/min
Example 1

22. Average Rate of Change
BUSINESS Refer to the graph below, which shows data on the fastest-growing restaurant chain in the U.S. during the time period of the graph. Find the rate of change of the number of stores from 2001 to 2006.
Example 2

23. Average Rate of Change
Answer:
Example 2

24. Average Rate of Change
Answer: Between 2001 and 2006, the number of stores in the U.S. increased at an average rate of 5.4(1000) or 5400 stores per year.
Example 2

25. A. increase of 3.25 million per year
COMPUTERS Refer to the graph. Find the average rate of change of the percent of households with computers in the United States from 2000 to 2004.
A. increase of 3.25 million per year
B. increase of 6.5 million per year
C. increase of 3.25% per year
D. increase of 13% per year
Example 2

26. A. increase of 3.25 million per year
COMPUTERS Refer to the graph. Find the average rate of change of the percent of households with computers in the United States from 2000 to 2004.
A. increase of 3.25 million per year
B. increase of 6.5 million per year
C. increase of 3.25% per year
D. increase of 13% per year
Example 2

27. Concept

28. Find the slope of the line that passes through (–1, 4) and (1, –2).
Find Slope Using Coordinates
Find the slope of the line that passes through (–1, 4) and (1, –2).
Slope Formula
(x1, y1) = (–1, 4), (x2, y2) = (1, –2)
Simplify.
Answer:
Example 3

29. Find the slope of the line that passes through (–1, 4) and (1, –2).
Find Slope Using Coordinates
Find the slope of the line that passes through (–1, 4) and (1, –2).
Slope Formula
(x1, y1) = (–1, 4), (x2, y2) = (1, –2)
Simplify.
Answer: –3
Example 3

30. Find the slope of the line that passes through (9, –3) and (2, 7).B. C. D.
Example 3

31. Find the slope of the line that passes through (9, –3) and (2, 7).B. C. D.
Example 3

32. Find the slope of the line shown at the right.
Find Slope Using a Graph
Find the slope of the line shown at the right.
Slope Formula
(x1, y1) = (–1, 0), (x2, y2) = (1, 1)
Simplify.
Answer:
Example 4

33. Find the slope of the line shown at the right.
Find Slope Using a Graph
Find the slope of the line shown at the right.
Slope Formula
(x1, y1) = (–1, 0), (x2, y2) = (1, 1)
Simplify.
Answer:
Example 4

34. Find the slope of the line.A. B. C. D.
Example 4

35. Find the slope of the line.A. B. C. D.
Example 4