Given normal random variable $X$ and $Y=aX+b$, the cumulative distribution function for $Y$ is $F_{Y}(y)=P(Y\leq y)$. Show that $F_{Y}(y)=P(X\leq\frac{y-b}{a})$.
I know that the cdf of the normal random variable is $\frac{1}{\sqrt{2}}\int_{-\infty}^{x}e^{-t^2/2}dt$ but I'm not sure how to go from there to the desired result.