Question

Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. Show your work.
Please help!

Answer 1

Answer:

y = (3/2)x + 8

Step-by-step explanation:

Hi

First let's find the slope of the given line by converting to slope-intercept form:-

2x + 3y = 9

3y = -2x + 9

y = (-2/3)x + 3

From this we see that the slope is -2/3.

The slope of a line perpendicular to this one will be - 1 /  (-2/3)

= 3/2.    ( because for a line and its perpendicular, the slopes' product = -1).

Using the point-slope form  to find the equation of this line

y - y1 = m(x - x1).  Here m = slope and (x1, y1) is a point on the line.

Plugging in the given values ,  m = 3/2 , x1 = -2 and y1 = 5:-

y - 5 = 3/2 (x - -2)

y - 5 = 3/2x + 3

y = (3/2)x + 8   which is the equation in slope-intercept form.