Question

Draw a line perpendicular to the line that contains the points

Answer 1

Answer:

$y=\frac{3}{2} x+\frac{20}{3}$

Step-by-step explanation:

First, to find the original line, employ the slope formula.

$\frac{y2-y1}{x2-x1} \\\\\frac{6-8}{4-1} \\\\\frac{-2}{3}$

The slope of your original line is $-\frac{2}{3}$.

Next, plug in your slope and the third point to the point-slope formula.

$y-y1=m(x-x1)\\\\y-8=-\frac{2}{3} (x+2)\\\\y-8=-\frac{2}{3} x-\frac{4}{3}\\\\y=-\frac{2}{3} x+\frac{20}{3}$

To find the line which is perpendicular to the line, take the opposite reciprocal of the slope.

To find the opposite, flip the sign. $-\frac{2}{3}$ is negative, so it will become $\frac{2}{3}$, which is positive.

To find the reciprocal, flip the fraction. $\frac{2}{3}$ would become $\frac{3}{2}$.

Your slope for the perpendicular line is $\frac{3}{2}$, so your line is:

$y=\frac{3}{2} x+\frac{20}{3}$