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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 3: Q36. (page 203)

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.
If $y = 鈭� 6$ when $x = 9$ , find x when $y = 鈭� 3$ .

Short Answer

Expert verified

The direct variation equation that relates x and y is $y = \frac{鈭� 2}{3} x$ and the value of x when $y = 鈭� 3$ is $\frac{9}{2}$ .

Step by step solution

01

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 $y 伪 x$ .

Therefore, it is obtained that:

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

Where k is constant of proportionality.

It is given that when $x = 9, y = 鈭� 6$ .

Therefore, substitute 9 for x and $- 6$ for y in the equation $y = k x$ to find the value of k.

$\begin{matrix} y = k x \\ 鈭� 6 = k (9) \\ \frac{鈭� 6}{9} = k \\ \frac{鈭� 2}{3} = k \end{matrix}$

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

Therefore, it is obtained that:

$\begin{matrix} y = k x \\ y = \frac{鈭� 2}{3} x \end{matrix}$

Therefore, the direct variation equation that relates x and y is $y = \frac{鈭� 2}{3} x$ .

02

Step 2. Find the value of x when y=−3.

The direct variation equation that relates x and y is $y = \frac{鈭� 2}{3} x$ .

Find the value of x by substituting $- 3$ for y in the equation $y = \frac{鈭� 2}{3} x$ .

$\begin{matrix} y = \frac{鈭� 2}{3} x \\ 鈭� 3 = \frac{鈭� 2}{3} x \\ 鈭� 9 = 鈭� 2 x \\ \frac{鈭� 9}{鈭� 2} = x \\ \frac{9}{2} = x \end{matrix}$

Therefore, the value of x when $y = 鈭� 3$ is $\frac{9}{2}$ .

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