Question

A line is perpendicular to y=2/3x+2/3 and intersects the point (-2,4). What is the equation of this perpendicular line?

Answer 1

Answer:

y = - $\frac{3}{2}$ x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{2}{3}$ x + $\frac{2}{3}$ ← is in slope- intercept form

with slope m = $\frac{2}{3}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{2}{3} }$ = - $\frac{3}{2}$

Using the point- slope form

with m = - $\frac{3}{2}$ and (x₁, y₁ ) = (- 2, 4) , then

y - 4 = - $\frac{3}{2}$ (x - (- 2) ) , that is

y - 4 = - $\frac{3}{2}$ (x + 2) ← distribute

y - 4 = - $\frac{3}{2}$ x - 3 ( add 4 to both sides )

y = - $\frac{3}{2}$ x + 1 ← in slope- intercept form