SOLUTION: Given the line y = 3x – 2 and the point (2, -4), find the equations of the lines parallel and perpendicular to the line above.

Algebra ->  Points-lines-and-rays -> SOLUTION: Given the line y = 3x – 2 and the point (2, -4), find the equations of the lines parallel and perpendicular to the line above.      Log On


   

Question 321919: Given the line y = 3x – 2 and the point (2, -4), find the equations of the lines parallel and perpendicular to the line above.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel lines have identical slopes.
y=3x%2Bb
Use the point (2,-4) to solve for b.
-4=3%282%29%2Bb
b%2B6=-4
b=-10
highlight%28y=3x-10%29
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Perpendicular lines have slopes that are negative reciprocals,
m1%2Am2=-1
3%2Am2=-1
m2=-1%2F3
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y=-%281%2F3%29x%2Bb
Again, use the point (2,-4) to solve for b,
-4=-2%2F3%2Bb
b=-12%2F3%2B2%2F3
b=-10%2F3
highlight%28y=-%281%2F3%29x-10%2F3%29
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Blue line is the original line.
Red line is the parallel line.
Green line is the perpendicular line.