2. Main Idea and New Vocabulary Example 1: Find a Constant Ratio
Key Concept: Direct Variation
Example 2: Solve a Direct Variation
Example 3: Identify Direct Variation
Example 4: Identify Direct Variation
Key Concept: Linear Functions
Lesson Menu

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

4. Find a Constant Ratio
FINANCIAL LITERACY The amount of money Serena earns at her job is shown on the graph. Determine the amount Serena earns per hour.
Example 1

5. Answer: Serena earns $10 per hour.
Find a Constant Ratio
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

6. SHOPPING The cost of softballs is shown on the graph
SHOPPING The cost of softballs is shown on the graph. Determine the cost per softball.
A. $0.27 per softball
B. $3.75 per softball
C. $6.00 per softball
D. $12.00 per softball
Example 1 CYP

7. Key Concept 2

8. 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 total cost.
y = kx Direct variation
5 = k(4) y = 5, x = 4
1.25 = k Simplify.
y = 1.25x Replace k with 1.25.
Example 2

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

10. SHOPPING The total cost for sports drinks varies directly as the number of bottles purchased. If 6 bottles cost $7.50, how much would it cost to buy 9 bottles?
A. $7.20
B. $10.00
C. $11.25
D. $15.00
Example 2 CYP

11. 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 the same. The function is not a direct variation.
Example 3

12. A. Yes; the constant of variation is 54.
Determine whether the linear function is a direct variation. If so, state the constant of variation.
A. Yes; the constant of variation is 54.
B. Yes; the constant of variation is –54.
C. No; the ratios are not proportional.
D. No; the ratios are not greater than 1.
Example 3 CYP

13. Identify Direct Variation
Determine whether the linear function is a direct variation. If so, state the constant of variation.
Example 4

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

15. A. Yes; the constant of variation is –32.5.
Determine whether the linear function is a direct variation. If so, state the constant of variation.
A. Yes; the constant of variation is –32.5.
B. Yes; the constant of variation is 32.5.
C. No; the ratios are not proportional.
D. No; the ratios are not greater than 1.
Example 4 CYP

16. Key Concept 5