+1694 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 $a + b$.
+1786 First, we know the equation of a sliope is \(\frac{y_2-y_1}{x_2-x_1}\)
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
\( [ b^2 - a^2 ] / [ b - a ]\)
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! :)
+1786 First, we know the equation of a sliope is \(\frac{y_2-y_1}{x_2-x_1}\)
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
\( [ b^2 - a^2 ] / [ b - a ]\)
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! :)
