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If $y$ varies directly with $x$ and $y = 21$ when $x = -3$ , find $y$ when $x = -2$ . Write and solve a direct variation equation to find the answer. $\newline$ y = ____

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Write and solve direct variation equations

Full solution

Q. If

y

varies directly with

x

and

y = 21

when

x = -3

, find

y

when

x = -2

. Write and solve a direct variation equation to find the answer.

\newline

y = ____

Given $y = 21$ : Given $y = 21$ when $x = -3$ . $\newline$ Substitute into $y = kx$ to find $k$ . $\newline$ $21 = k(-3)$ .
Substitute and solve for $k$ : Divide both sides by $-3$ to solve for $k$ . $k = \frac{21}{-3}.$ $k = -7.$
Direct variation equation: Direct variation equation with $k$ : $y = -7x$ . $\newline$ Find $y$ when $x = -2$ . $\newline$ Substitute $-2$ for $x$ in $y = -7x$ . $\newline$ $y = -7(-2)$ .
Find $y$ for $x = -2$ : Calculate $y$ . $\newline$ $y = 14$ .

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\newline

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