Question

a line with a slope of -1/4 passes through the points (n,6) and (-4,9). what is the value of n?

Answer 1

The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:

$m=\frac{y_2-y_1}{x_2-x_1}$

Replacing with the points (n,6) and (-4,9), and with m = -1/4, we get:

$\begin{gathered} -\frac{1}{4}=\frac{9-6}{-4-n} \\ -\frac{1}{4}=\frac{3}{-4-n} \\ (-1)\cdot(-4-n)=3\cdot4 \\ (-1)\cdot(-4)+(-1)\cdot(-n)=12 \\ 4+n=12 \\ n=12-4 \\ n=8 \end{gathered}$