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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

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

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

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

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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

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

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

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

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

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

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

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

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

(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

(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

(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

(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

(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

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

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