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If $y$ varies directly with $x$ and $y = 12$ when $x = 6$ , find $y$ when $x = 4$ . $\newline$ 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 = 12

when

x = 6

, find

y

when

x = 4

.

\newline

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

\newline

y =

____

Substitute values into equation: Now, plug in the values $y = 12$ and $x = 6$ to find $k$ . $12 = k \times 6$
Solve for k: Divide both sides by $6$ to solve for k. $\newline$ $k = \frac{12}{6}$ $\newline$ $k = 2$
Final direct variation equation: Now we have the direct variation equation $y = 2x$ . $\newline$ Let's find $y$ when $x = 4$ . $\newline$ $y = 2 \times 4$
Find y value: Do the multiplication to find $y$ . $y = 8$

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