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Question 160256: Line l is perpendicular to the graph of the equation -6x - 5y = 30 and contains the point (2, -5). Find the equation for l.
y =
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Line l is perpendicular to the graph of the equation -6x - 5y = 30 and contains the point (2, -5). Find the equation for l.
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Determine slope of:
-6x - 5y = 30
Do this by converting into y=mx+b:
-6x - 5y = 30
- 5y = 6x+30
y = (-6/5)x - 6
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Now, we know the slope is -6/5
A line perpendicular is negative reciprocal:
m(-6/5) = -1
m(6/5) = 1
m = 5/6 (our slope for the new line)
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Given a point (2, -5) and a slope 5/6, plug it into the "point-slope" form:
y – y1 = m(x – x1)
y – (-5) = (5/6)(x – 2)
y+5 = (5/6)(x – 2)
6y+30 = 5(x – 2)
6y+30 = 5x – 10
6y = 5x – 40
y = (5/6)x – (40/6)
y = (5/6)x – (20/3)
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