 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.

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Direct Variation and Proportion

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Presentation transcript:

 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  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

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

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

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

 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.

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.

In order to solve proportions, cross multiply!

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?

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

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

The wages for a worker at a particular store are hourly. A person who worked 18 hours earned $ 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

Sec 1.4 p even