+1855 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 First, we know the equation of a sliope is y2−y1x2−x1
In this problem, we know the two points we have are (a, a^2) and (b, b^2).
Plugging these two points in, we get
[b2−a2]/[b−a]
Using the difference of squares equation for the numerator, we have
[(b−a)(b+a)]/(b−a)
Notice the b - a cancel each other out.
This leaves us with
b+a
Since the slope is 2, we simplfy have
b+a=2
So the answer is 2.
Thanks! :)
+1946 First, we know the equation of a sliope is y2−y1x2−x1
In this problem, we know the two points we have are (a, a^2) and (b, b^2).
Plugging these two points in, we get
[b2−a2]/[b−a]
Using the difference of squares equation for the numerator, we have
[(b−a)(b+a)]/(b−a)
Notice the b - a cancel each other out.
This leaves us with
b+a
Since the slope is 2, we simplfy have
b+a=2
So the answer is 2.
Thanks! :)
