1. Splash Screen

2. Five-Minute Check (over Lesson 9–4) Main Idea and Vocabulary
Example 1: Real-World Example: Find a Constant Ratio
Key Concepts: Direct Variation
Example 2: Real-World Example: Solve a Direct Variation
Example 3: Identify Direct Variation
Example 4: Identify Direct Variation
Concept Summary: Proportional Linear Function
Lesson Menu

3. Use direct variation to solve problems.
constant of variation
Main Idea/Vocabulary

4. Answer: Serena earns $10 per hour.
Find a Constant Ratio
EARNINGS The amount of money Serena earns at her job varies directly as the number of hours she works. Determine the amount Serena earns per hour.
Since the graph of the data forms a line, the rate of change is constant. Use the graph to find the constant ratio.
Answer: Serena earns $10 per hour.
Example 1

5. EARNINGS The amount of money Elizabeth earns at her job varies directly as the number of hours she works. Determine the amount Elizabeth earns per hour.
$8 per hour
$10 per hour
$12 per hour
D. $15 per hour A B C D
Example 1

6. KC

7. Solve a Direct Variation
SHOPPING The total cost for cans of soup varies directly as the number of cans purchased. If 4 cans of soup cost $5, how much would it cost to buy 8 cans?
Write an equation of direct variation. Let x represent the number of cans and let y represent the cost.
y = kx Direct variation
5 = k(4) y = 5, x = 4
1.25 = k Simplify.
y = 1.25x Substitute for k = 1.25.
Example 2

8. Solve a Direct Variation
Use the equation to find y when x = 8.
y = 1.25x
y = 1.25(8) x = 8
y = 10 Multiply.
Answer: It would cost $10 to buy 8 cans.
Example 2

9. SHOPPING The cost for apples varies directly as the number of apples purchased. A grocery store sells 6 apples for $2.70. How much would it cost to buy 10 apples?
A. $4.50
B. $4.85
C. $5.00
D. $5.20 A B C D
Example 2

10. Identify Direct Variation
Determine whether the linear function is a direct variation. If so, state the constant of variation.
Compare the ratios to check for a common ratio.
Answer: The ratios are not proportional, so the function is not a direct variation.
Example 3

11. Determine whether the linear function is a direct variation
Determine whether the linear function is a direct variation. If so, state the constant of variation.
A. yes;
B. yes; 8
C. yes; 4
D. no A B C D
Example 3

12. Identify Direct Variation
Determine whether the linear function is a direct variation. If so, state the constant of variation.
Compare the ratios to check for a common ratio.
Example 4

13. Identify Direct Variation
Answer: Since the ratios are proportional, the function is a direct variation. The constant of variation is or 8.5.
Example 4

14. Determine whether the linear function is a direct variation
Determine whether the linear function is a direct variation. If so, state the constant of variation.
A. yes;
B. yes; 6
C. yes;
D. no A B C D
Example 4

15. CS

16. End of the Lesson
End of the Lesson

17. Five-Minute Check (over Lesson 9–4) Image Bank Math Tools
Slope and Intercept
Resources

18. (over Lesson 9-4)
Find the slope of the line that passes through the points A(0, 0) and B(4, 3). A. B. C. D. A B C D
Five Minute Check 1

19. (over Lesson 9-4)
Find the slope of the line that passes through the points M(–3, 2) and N(7, –5). A. B. C. D. A B C D
Five Minute Check 2

20. (over Lesson 9-4)
Find the slope of the line that passes through the points P(–6, –9) and Q(2, 7).
A. –2 B. C.
D. 2 A B C D
Five Minute Check 3

21. (over Lesson 9-4)
Find the slope of the line that passes through the points K(6, –3) and L(16, –4).
A. 10 B. C.
D. –10 A B C D
Five Minute Check 4

22. (over Lesson 9-4)
Do the points A(5, 4), B(10, 4), C(5, –1), D(0, 0) form a parallelogram when they are connected? Explain. (Hint: Two lines that are parallel have the same slope.) A. B. A B
Five Minute Check 5

23. Refer to the figure. What is the slope of the graph?
(over Lesson 9-4)
Refer to the figure. What is the slope of the graph?
A. 3 B. C.
D. –3 A B C D
Five Minute Check 6

24. End of Custom Shows