SOLUTION: Write the slope intercept equation for the line that passes through (-2,3) and is perpendicular to 2x-9y=-12 Please show your work

Algebra ->  Linear-equations -> SOLUTION: Write the slope intercept equation for the line that passes through (-2,3) and is perpendicular to 2x-9y=-12 Please show your work      Log On


   

Question 651935: Write the slope intercept equation for the line that passes through (-2,3) and is perpendicular to 2x-9y=-12 Please show your work
Answer by VirtualMathTutor(26) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F9 + 2x%2F9
Simplify
y = 4%2F3 + 2x%2F9
Now compare to y = mx + b
so the slope m = 2%2F9
Slope of the line perpendicular to the given line will then be the negative reciprocal of 2%2F9 which is -9%2F2
Now find the equation of the line passing through (-2, 3)
Use the formula y - y1 = m(x - x1)
y - 3 = -9%2F2(x -(-2))
y - 3 = -9%2F2x - 9
Add 3 to both sides:
y = -9%2F2x - 6