+1493 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 $a + b$.
+1946 Let's first focus on the slope of the line introduced.
First, note that the slope of a line is in the form y2−y1x2−x1
Thus, plugging in the two points we have, we get
[b2−a2]/[b−a]=2
Now, using the difference of squares thereom, we can simpplify the top to
[(b−a)(b+a)]/(b−a)=2
The b-a cancels out, leaving us with
b+a=2
So 2 is our answer.
Thanks! :)
