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Bellwork

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?. Lesson 1.4. Direct Variation and Proportion. Direct Variation.

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Bellwork

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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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