A line has a slope of $-7$ and contains the point $(3,0)$. The equation of this line can be written in the form $y = mx+b$. What is the value of $m+b$?
I know that the slope of a line is the coefficient of $x$ in the equation $y = mx+b$, so $m = -7$. I also know that the point $(3,0)$ lies on the line, so I can plug in those values of $x$ and $y$ into the equation and solve for $b$. So I have $0 = -7 \cdot 3 + b$, which simplifies to $0 = -21 + b$. Adding $21$ to both sides, I get $b = 21$. Therefore, the equation of the line is $y = -7x + 21$, and the value of $m+b$ is $-7 + 21 = 14$. 