Question

What is the equation of the line that is perpendicular to line m and passes through the point (3, 2)?

Answer 1

Answer:

y = $\frac{2}{5}$ x + $\frac{4}{5}$

Step-by-step explanation:

Calculate the slope of line m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m = $\frac{-3-2}{0-(-2)}$ = $\frac{-5}{0+2}$ = - $\frac{5}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{5}{2} }$ = $\frac{2}{5}$ , then

y = $\frac{2}{5}$ x + c ← is the partial equation in slope- intercept form

To find c substitute (3, 2 ) into the partial equation

2 = $\frac{6}{5}$ + c ⇒ c = 2 - $\frac{6}{5}$ = $\frac{4}{5}$

y = $\frac{2}{5}$ x + $\frac{4}{5}$ ← equation of perpendicular line