Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.
Using the slope formula gives b2−a2b−a=2.
Note that b2−a2=(b−a)(a+b) by difference of squares formula. Then, simplifying, we have
(b−a)(a+b)b−a=2a+b=2