Question 651935
Two lines are perpendicular when the slopes are the negative reciprocal of each other.

The line given is: 2x - 9y = -12

First, find the slope by solving for y:


2x - 9y = -12

Subtract 2x from both sides:

2x - 9y - 2x = -12 - 2x

-9y = -12 - 2x

Divide both sides by -9

y = {{{12/9}}} + {{{2x/9}}}

Simplify

y = {{{4/3}}} + {{{2x/9}}}

Now compare to y = mx + b

so the slope m = {{{2/9}}}

Slope of the line perpendicular to the given line will then be the negative reciprocal of {{{2/9}}} which is {{{-9/2}}}

Now find the equation of the line passing through (-2, 3)

Use the formula y - y1 = m(x - x1)

y - 3 = {{{-9/2}}}(x -(-2))

y - 3 = {{{-9/2}}}x - 9
Add 3 to both sides:

y = {{{-9/2}}}x - 6