Question

what is the slope of all lines perpendicular to this line? (3, 10) (0, 4) +2 2 -1/2 1/2

Explanation:

Step1: Find the slope of the given line

Use the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, with $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(3,10)$. So $m=\frac{10 - 4}{3-0}=\frac{6}{3}=2$.

Step2: Find the slope of the perpendicular line

The slope of a line perpendicular to a line with slope $m$ is $-\frac{1}{m}$. Since the slope of the given line is $2$, the slope of the perpendicular line is $-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$