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Main Idea/Vocabulary

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

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Main Idea/Vocabulary

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

  2. Find a Constant Ratio EARNINGSThe 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

  3. A B C D 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 Example 1

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  5. Solve a Direct Variation SHOPPINGThe 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

  6. 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

  7. A B C D SHOPPINGThe 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 Example 2

  8. 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

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

  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. Example 4

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

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

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

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

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

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

  18. A B A. B. (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.) Five Minute Check 5

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

  20. End of Custom Shows

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