Question

Let $P=(a,b)$ be the point of intersection of the line $y=2x-10$ and the line through $(7,8)$ and $(9,0)$. Compute $a+b$.

Answer 1

The second line has slope (0−8)/(9−7)=−4, so its equation is y−8=−4(x−7) ⇒ y=−4x+36. Solve 2x−10=−4x+36 ⇒ 6x=46 ⇒ x=23/3, y=16/3. Thus a+b=23/3+16/3=13.