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If $y$ varies directly with $x$ and $y = 63$ when $x = 7$ , find $y$ when $x = 4$ . Write and solve a direct variation equation to find the answer. Simplify any fractions. $\newline$ y = ____

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Write and solve direct variation equations

Full solution

Q. If

y

varies directly with

x

and

y = 63

when

x = 7

, find

y

when

x = 4

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

\newline

y = ____

Plug in values: Now, we plug in the values we know, $y = 63$ and $x = 7$ , into the equation to find $k$ . So, $63 = k \times 7$ .
Find $k$ : To find $k$ , we divide both sides by $7$ . So, $k = \frac{63}{7}$ , which gives us $k = 9$ .
Substitute $x$ : Now we have the direct variation equation $y = 9x$ . We need to find $y$ when $x = 4$ . So we substitute $x$ with $4$ into the equation, $y = 9 \times 4$ .
Calculate $y$ : After the calculation, we get $y = 36$ . So, when $x = 4$ , $y = 36$ .

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