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 $m+b$?
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*}
0&=-7(3)+b\\
\Rightarrow\qquad 0&=-21+b\\
\Rightarrow\qquad 21&=b
\end{align*} Therefore, the value of $m+b$ is $-7+21=\boxed{14}$.
14
Level 3
Algebra
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 $m+b$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the equation of the line, we start with the slope-intercept form, which is given by the equation \(y = mx + b\). Here, \(m\) represents the slope of the line, and \(b\) represents the y-intercept. 

Given that the slope \(m\) is \(-7\), we can substitute this value into the equation, resulting in \(y = -7x + b\). 

Next, we need to determine the value of \(b\). We know that the line passes through the point \((3, 0)\). This means that when \(x = 3\), \(y\) must equal \(0\). We can substitute these coordinates into the equation to solve for \(b\):

\[
0 = -7(3) + b
\]

Calculating the right side gives:

\[
0 = -21 + b
\]

To isolate \(b\), we add \(21\) to both sides:

\[
b = 21
\]

Now we have both \(m\) and \(b\): \(m = -7\) and \(b = 21\). 

To find \(m + b\), we perform the addition:

\[
m + b = -7 + 21
\]

Calculating this gives:

\[
m + b = 14
\]

Thus, the final answer is \(14\).<|END_OF_LATENT|> The final answer is $14$.