What is an equation of the line that is perpendicular to the line y=-2/3x-1 and passes through the point (-4,2)

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Answer 1

Perpendicular lines have negative reciprocal slopes. So the slope of the line we are looking for is 3/2 since that is the negative reciprocal of -2/3. So far we know that our line will have the equation y = 3/2x +b. The line has to pass through the point (-4,2) so we can use that to find b:

 

2 = (3/2)*-4 + b

 

2 = -6 + b

8 = b

 

Now we can write the equation of the perpendicular line as:

 

y = (3/2)x + 8