The graph of the line $x+y=b$ intersects the line segment from $(2,5)$ to $(4,9)$ at its midpoint. What is the value of $b$?
That means the midpoint is $(\frac{2+4}{2}, \frac{5+9}{2})$, which simplifies to $(3,7)$. Now, I know that the line $x+y=b$ passes through this point, so I can plug in the coordinates and solve for $b$. I get $3+7=b$, which implies that $b=10$. 