SOLUTION: Write an equation of the line described. Through (-6,3), perpendicular to -2x+3y=3

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Question 127452: Write an equation of the line described.

Through (-6,3), perpendicular to -2x+3y=3
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Fiest we need to find the slope of the line:
-2x+3y=3 or 3y=2x+3 or y=2x/3+3/3 or y=2x/3+1 (red line)the slope of this line is 2/3.
For a line to be perpendicular to this line it has to ahve a slope of -3/2.
If it passes through (-6,3) then the equation is:
3=-6(-3/2)+b where b is the y intercept.
3=18/2+b
3=9+b
b=3-9
b=-6.
Thus this line equation is:
y=-3x/2-6 (green line)
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2F3+%2B1%2C+-3x%2F2-6%29+ (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions 2x/3 +1 and -3x/2 -6).