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If $y$ varies directly with $x$ and $y = 84$ when $x = 12$ , find $y$ when $x = 6$ . 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 = 84

when

x = 12

, find

y

when

x = 6

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

\newline

y = ____

Substitute and Solve: Given $y = 84$ when $x = 12$ , substitute into $y = kx$ to find $k$ . $84 = k \times 12$
Calculate $k$ : Divide both sides by $12$ to solve for $k$ . $k = \frac{84}{12}$ $k = 7$
Find Direct Variation Equation: Now we have $k$ , so the direct variation equation is $y = 7x$ . $\newline$ To find $y$ when $x = 6$ , substitute $x = 6$ into $y = 7x$ . $\newline$ $y = 7 \times 6$
Substitute $x = 6$ : Calculate the value of $y$ . $\newline$ $y = 42$

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