Question

First using point slope form, write the equation of the line in slope-intercept form

Answer 1

Answer:

y = $\frac{2}{3}$ x - 8

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

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

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

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

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = $\frac{2}{3}$ and (a, b) = (9, - 2), thus

y - (- 2) = $\frac{2}{3}$(x - 9), that is

y + 2 = $\frac{2}{3}$(x - 9) ← in point- slope form

Distribute right side and rearrange

y + 2 = $\frac{2}{3}$ x - 6 ( subtract 2 from both sides )

y = $\frac{2}{3}$ x - 8 ← in slope- intercept form