### Instruction: The line $y = \frac{1}{2} x + 4$ is paramterized by the form
\[\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -7 \\ s \end{pmatrix} + t \begin{pmatrix} l \\ -5 \end{pmatrix}.\]Enter the ordered pair $(s,l).$.### Response: I notice that the line has a slope of $\frac{1}{2}$, which means that the ratio of the vertical and horizontal changes is $\frac{1}{2} = \frac{-5}{l}$.
So I can solve for $l$ by cross-multiplying: $l = -10$.
Now I need to find $s$, which is the y-coordinate when $x = -7$ and $t = 0$.
I can plug in $x = -7$ into the original equation of the line and get $y = \frac{1}{2} (-7) + 4 = 0.5$.
This means that $s = 0.5$.
So the ordered pair is $(0.5, -10)$.