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Direct Variation and Proportion

Direct Variation and Proportion. Section 1.4. A ratio is the comparison of two quantities by division. Ex. is read as “a is to b” A proportion is a statement that two ratios are equal. Ex. as read as “a is to b as c is to d”. Cross Product Property of Proportions For

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Direct Variation and Proportion

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  1. Direct Variation and Proportion Section 1.4

  2. A ratio is the comparison of two quantities by division. • Ex. is read as “a is to b” • A proportion is a statement that two ratios are equal. • Ex. as read as “a is to b as c is to d”

  3. Cross Product Property of Proportions • For • If , then ad = bc • Important to check answers, sometimes the answer will not work because it causes one of the denominators to equal zero

  4. Solve each proportion for the variable. Check your answers. • Ex.

  5. Ex.

  6. Ex.

  7. Why learn about direct variation? • Many situations in real life when one quantity varies directly as the result of another. • Such as • Distance traveled • Paychecks of hourly workers • Tax paid on purchase

  8. Direct Variation • The variable y varies directly as x if there is a nonzero constant k such that y = kx. • The equation y = kx is called a direct variation equation. • K is called the constant of variation

  9. Find the constant of variation, k if y varies directly as x and y = -72 when x = -18. • y = kx • -72 = k(-18) • k = 4

  10. Find the constant of variation, k if y varies directly as x and y = 2/3 when x = 1/3.

  11. Write an equation of direct variation that relates the two variables. • y = 7 for x = 3

  12. Y = 3.2 for x = 12.8

  13. Each day Jonathon rides his bicycle for exercise. When traveling at a constant rate, he rides 4 miles in about 20 minutes. At this rate, how ling would it take him to ride 7 miles? • Distance = (rate)(time) • Find his rate • Use that rate to solve for his new distance.

  14. That problem also could have been solved using a proportion. • Proportion property of direct variation: For • If satisfy y = kx, then

  15. The speed of sound in air is about 335 ft per second. At this rate, how far would sound travel in 25 seconds?

  16. Julie works for an hourly wage. Last week she worked 18 hours and earned before taxes $150.30. • How many hours must Julie work to earn $208.75? • Write the direct variation equation that gives Julie’s income in terms of hours worked. What does the constant of variation represent?

  17. Day 2 • a varies directly as b • If a is 6.3 when b is 70, find b when a is 5.4. • If b is 3/5 when a is 9/10, find a when b is 1/3.

  18. Determine whether the values in the table represent a direct variation. If so, write an equation for the variation. If not, explain.

  19. Ex.

  20. Ex.

  21. Ex.

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