## College Algebra (11th Edition)

$y=-30$
$\bf{\text{Solution Outline:}}$ Use $y=kx$ and solve for the value of $k$ with the given $x$ and $y$ values. Then use the equation of variation to solve for the value of the unknown variable. $\bf{\text{Solution Details:}}$ Since $y$ varies directly as $x$, then $y=kx.$ Substituting the given values, $y=20$ and $x=4 ,$ then the value of $k$ is \begin{array}{l}\require{cancel} 20=k(4) \\\\ \dfrac{20}{4}=k \\\\ k=5 .\end{array} Hence, the equation of variation is given by \begin{array}{l}\require{cancel} y=kx \\\\ y=5x .\end{array} If $x=-6,$ then \begin{array}{l}\require{cancel} y=5x \\\\ y=5(-6) \\\\ y=-30 .\end{array}