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

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

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

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

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

Key Concept 2

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

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

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

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

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

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

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

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

Key Concept 5