SOLUTION: Find an equation of a line passing through (-1,1) and perpendicular to the line whose equation is given by 3x-2y=1.

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Question 56642: Find an equation of a line passing through (-1,1) and perpendicular to the line whose equation is given by 3x-2y=1.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of a line passing through (-1,1) and perpendicular to the line whose equation is given by 3x-2y=1.
First find the slope of the equation by putting it in slope intercept form:highlight%28y=mx%2Bb%29, where m=slope and (0,b)=y-intercept:
3x-2y=1
-3x%2B3x-2y=-3x%2B1
-2y=-3x%2B1
-2y%2F-2=-3x%2F-2%2B1%2F-2
y=%283%2F2%29x-1%2F2
y=highlight%28%283%2F2%29%29x-1%2F2, the slope,m=3/2.
Perpendicular equations have slopes that are negative reciprocals of each other, so flip the slope over and change its sign.
We need a line with a slope, m=-2/3 going through the point (x1,y1)=(-1,1).
We need to use the point slope formula highlight%28y-y1=m%28x-x1%29%29.
y-1=%28-2%2F3%29%28x-%28-1%29%29
y-1=%28-2%2F3%29%28x%2B1%29
y-1=%28-2%2F3%29x-%282%2F3%29%281%29
y-1=%28-2%2F3%29x-2%2F3
y-1%2B1=%28-2%2F3%29x-2%2F3%2B1
y=%28-2%2F3%29x-2%2F3%2B3%2F3
y=%28-2%2F3%29x%2B%28-2%2B3%29%2F3
y=%28-2%2F3%29x%2B1%2F3 <--Slope intercept form
3y=-2x%2B1
2x%2B3y=1 <--Standard form
Happy Calculating!!!