In the line $4x+7y+c=0$, the sum of the $x$- and $y$- intercepts is $22$. Find $c$.
I want to find the $x$- and $y$- intercepts of the line and then add them up to get $22$. To find the $x$-intercept, I plug in $y=0$ and solve for $x$. I get $4x+c=0$, so $x=-c/4$. To find the $y$-intercept, I plug in $x=0$ and solve for $y$. I get $7y+c=0$, so $y=-c/7$. Adding up the intercepts, I get $-c/4-c/7=22$. Multiplying both sides by $28$, I get $-7c-4c=616$. Simplifying, I get $-11c=616$, so $c=-56$. 