| { | |
| "problem": "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 $m+b$?", | |
| "level": "Level 3", | |
| "type": "Algebra", | |
| "solution": "First, remember that the slope of a line in the form of $y=mx+b$ is equal to $m$. So, the line must take the form $y=-7x+b$. Next, substitute the point $(3,0)$ and solve for $b$: \\begin{align*}\n0&=-7(3)+b\\\\\n\\Rightarrow\\qquad 0&=-21+b\\\\\n\\Rightarrow\\qquad 21&=b\n\\end{align*} Therefore, the value of $m+b$ is $-7+21=\\boxed{14}$." | |
| } |