How do I show for nonzero constants $a$ and $b$ that $\operatorname{Corr} (x,y) = -1$ or $1$?

Question

Let $X$ be a random variable with a mean of $\mu$ and a variance of $\sigma^2$ and let $Y = aX +b$. Show for non-zero constants $a$ and $b$ that $\operatorname{Corr}(X; Y ) = +1$ or $-1$.

Answer 1

Use the fact that $$\text{Corr}(X,Y) = \frac{\text{Cov}(X,Y)}{\sigma_{X} \sigma_{Y}}$$