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Direct Variation and Proportions | Understanding Constants in Math Equations

Explore direct variation and proportions in math, solving equations to find constants and understand how variables react. Practice with examples and applications. Get ready with direct variation and proportions homework!

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Direct Variation and Proportions | Understanding Constants in Math Equations

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  1. Bellwork • In the isosceles triangle below, AB = CB. What is the measure of the vertex angle if the measure of angle A is 40 degrees? • What is the sum of a and h in the diagram below?

  2. Lesson 1.4 Direct Variation and Proportion

  3. Direct Variation As I work more hours what happens to my weekly wage? What fact remains constant in this example? My wages If I get a raise at work, what happens to the amount of income tax I will have to pay? What fact remains constant in this example? Tax rate

  4. Direct Variation y = k x In these examples, a constant causes a variable to react in the same way. This is called the Constant of Variation

  5. Objective: Given information for x and y find the constant of variation write the direct variation equation

  6. Example: If y varies directly as x and y = -72 when x = -18, find the constant of variation and write the direct variation equation. Step 1: Find k y = k x -72 = k (-18) k = 4 Step 2: Write the direct variation equation y = 4x

  7. Try some: • Y varies directly as x. If y = -4 when x = 5, find the constant of variation and write the direct variation equation. • If x and y vary directly and y = 1/2 when x = 6, find the constant of variation and write the direct variation equation. • a varies directly as b. If a is 7 when b is ¾, find the constant of variation and write the direct variation equation.

  8. Proportions It is said that if y varies directly as x, then y is proportional to x. A proportion is a statement that 2 ratios are equal.

  9. Solving Proportions In order to solve proportions, cross multiply!

  10. Application: When traveling at a constant rate, Adria drive her car 12 miles in about 15 minutes. At this rate how long would it take Adria to drive 30 miles?

  11. Application: If you leave your car in a parking garage and pay $30 for 7 and a half hours, how much would you pay if you left your car for 18 hours? ANS: $72

  12. Application: The speed of sound in air is about 335 feet per second. At this rate, how far would sound travel in 25 seconds? ANS: 8375 ft

  13. Application: The wages for a worker at a particular store are hourly. A person who worked 18 hours earned $114.30. • How many hours must this person work to earn $127? • ANS: 20 hours • Write a direct variation equation that gives the income of this person in terms of the hours worked. • ANS: y = 6.35 x

  14. Homework Sec 1.4 p. 33 14-50 even

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