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Q35.

Expert-verifiedFound in: Page 203

Book edition
Student Edition

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

Pages
801 pages

ISBN
9780078884801

**Suppose y **

**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**.

It is given that *y* varies directly as *x*.

Therefore it implies that $y\alpha x$.

Therefore, it is obtained that:

$\begin{array}{l}y\alpha x\\ y=kx\end{array}$

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 $y=kx$ to find the value of *k*.

$\begin{array}{c}y=kx\\ 15=k\left(2\right)\\ \frac{15}{2}=k\end{array}$

Substitute the value of *k* in the equation $y=kx$.

Therefore, it is obtained that:

$\begin{array}{c}y=kx\\ y=\frac{15}{2}x\end{array}$

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

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 $y=\frac{15}{2}x$.

$\begin{array}{c}y=\frac{15}{2}x\\ y=\frac{15}{2}\left(8\right)\\ y=15\left(4\right)\\ y=60\end{array}$

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

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