Doubling $x$ will cause the value of $y$ to double because in a direct variation, the change applied to one variable will result to the same change in the other variable.
Work Step by Step
RECALL: When $y$ varies directly as $x$, the equation of the variation is $y=kx$ . Doubling $x$ means $2x$ so replacing $x$ with $2x$ gives: $y=k(2x) \\y=2kx$ Notice that $2kx$ is twice of $kx$ Thus, doubling $x$ causes $y$ to double its value. This is because in a direct variation, whatever change is made to the value of $x$ will result to the same direct change in the value of $y$.