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If $y$ varies directly with $x$ and $y = -26$ when $x = 26$ , find $y$ when $x = 21$ . 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 = -26

when

x = 26

, find

y

when

x = 21

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

\newline

y = ____

Given values: Given $y = -26$ when $x = 26$ . $\newline$ Substitute into $y = kx$ to find $k$ . $\newline$ $-26 = k \times 26$ .
Calculate $k$ : Solve for $k$ . $k = \frac{-26}{26}$ . $k = -1$ .
Direct variation equation: Direct variation equation with $k$ : $y = -1x$ . Find $y$ when $x = 21$ . Substitute $21$ for $x$ in $y = -1x$ . $y = -1 \times 21$ .
Substitute $x$ : Calculate $y$ . $y = -21$ .

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