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If $y$ varies directly with $x$ and $y = -100$ when $x = -25$ , find $y$ when $x = 22$ . 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 = -100

when

x = -25

, find

y

when

x = 22

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

\newline

y = ____

Plug values into equation: We know $y = -100$ when $x = -25$ . Let's plug these values into the equation to find $k$ . $\newline$ $-100 = k(-25)$
Solve for k: Now, solve for k. $\newline$ $k = \frac{-100}{-25}$ $\newline$ $k = 4$
Write direct variation equation: We got $k = 4$ . Now, let's write the direct variation equation with our $k$ value. $\newline$ $y = 4x$
Substitute $x$ into equation: We need to find $y$ when $x = 22$ . Substitute $x = 22$ into the equation. $\newline$ $y = 4(22)$
Find $y$ : Now, do the multiplication to find $y$ . $y = 88$

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