Answer
$B$
Work Step by Step
We are given the two points, $(8, k)$ and $(7, -3)$. We are also given that the numerical value of the slope is $m = 5$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$,
where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line.
Let's plug in the values into this formula:
$5 = \frac{-3 - k}{7 - 8}$
Subtract the numerator and denominator to simplify:
$5 = \frac{-3 - k}{-1}$
Divide the numerator and denominator by their greatest common factor, which is $-1$:
$5 = 3 + k$
To solve for $k$, we subtract $3$ from each side of the equation:
$3 - 3 + k = 5 - 3$
Subtract to simplify:
$k = 2$
This answer corresponds to option $B$.
