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if $x$ is directly proportional to $y^2$ and $x=32$ when $y=2$ find an equation connecting $x$ and $y$

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Write direct variation equations

Full solution

Q. if

x

is directly proportional to

y^2

and

x=32

when

y=2

find an equation connecting

x

and

y

Write Equation: Write the direct variation equation. $x = ky^2$
Plug in Values: Plug in the given values, $x = 32$ and $y = 2$ , to find $k$ . $32 = k(2)^2$
Solve for k: Solve for k. $\newline$ $32 = k \times 4$ $\newline$ $k = \frac{32}{4}$ $\newline$ $k = 8$
Final Equation: Write the final equation using the value of $k$ . $x = 8y^2$

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