imc

Substitute the points $(2,3)$ and $(4,3)$ into the given equation for $(x,y)$. Then we get a system of two equations: $3=4+2b+c$ $3=16+4b+c$ Subtracting the first equation from the second we have: $0=12+2b$ $b=-6$ Then using $b=-6$ in the first equation: $0=1+-12+c$ $c=\boxed{11}$.