Answer
$x = 6$
Work Step by Step
When $y$ varies directly as $x$, the relationship is represented by an equation in the form $y=kx$ where $k$ is the constant of variation.
When $x = -\frac{2}{5}$, then $y = -3$. Substitute these values into $y=kx$ to find the value of $k$:
$-3 = k(-\frac{2}{5})$
Multiply both sides by $-\frac{5}{2}$ to solve for $k$:
$-3\left(-\frac{5}{2}\right) = k(-\frac{2}{5})\left(-\frac{5}{2}\right)\\
\frac{15}{2}=k$
The direct variation is represent by the equation $y=\frac{15}{2}x$.
To find the value of $x$ when $y=45$, substitute $45$ into $y$ to obtain:
$45 = \frac{15}{2}x\\
45\left(\frac{2}{15}\right)=\frac{15}{2}x\left(\frac{15}{2}\right)\\
\frac{90}{15}=x\\
6=x$
