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Q35.

Expert-verified

Algebra 1

Found in: Page 203

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 15$ when $x = 2$ , find y when $x = 8$ .

The direct variation equation that relates x and y is $y = \frac{15}{2} x$ .

The value of y when $x = 8$ is 60.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write a direct variation equation that relates x and y.

It is given that y varies directly as x.

Therefore it implies that $y α x$ .

Therefore, it is obtained that:

$\begin{array}{l} y α x \\ y = k x \end{array}$

Where k is constant of proportionality.

It is given that when $x = 2$ , $y = 15$ .

Therefore, substitute 2 for x and 15 for y in the equation $y = k x$ to find the value of k.

$\begin{matrix} y = k x \\ 15 = k (2) \\ \frac{15}{2} = k \end{matrix}$

Substitute the value of k in the equation $y = k x$ .

Therefore, it is obtained that:

$\begin{matrix} y = k x \\ y = \frac{15}{2} x \end{matrix}$

Therefore, the direct variation equation that relates x and y is $y = \frac{15}{2} x$ .

Step 2. Find the value of y when x=8.

The direct variation equation that relates x and y is $y = \frac{15}{2} x$ .

Find the value of y by substituting 8 for x in the equation $y = \frac{15}{2} x$ .

$\begin{matrix} y = \frac{15}{2} x \\ y = \frac{15}{2} (8) \\ y = 15 (4) \\ y = 60 \end{matrix}$

Therefore, the value of y when $x = 8$ is 60.

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