SOLUTION: Write the equation of a line that is perpendicular to the given line and that passes through the given point: y=2/3x+9;(-6,5)

Algebra ->  Linear-equations -> SOLUTION: Write the equation of a line that is perpendicular to the given line and that passes through the given point: y=2/3x+9;(-6,5)      Log On


   

Question 306870: Write the equation of a line that is perpendicular to the given line and that passes through the given point:
y=2/3x+9;(-6,5)
Found 2 solutions by Fombitz, texttutoring:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Perpendicular lines have slopes that are negative reciprocals.
+m1=2%2F3
m1%2Am2=-1
m2=-3%2F2
y=-%283%2F2%29x%2Bb
Use the point (-6,5) to solve for b.
5=-%283%2F2%29%28-6%29%2Bb
5=9%2Bb
b=-4
highlight_green%28y=-%283%2F2%29x-4%29
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Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
Perpendicular lines have slopes that are negative reciprocals of each other.

The original line has a slope of m=2/3, so a line perpendicular to it will have a slope of m=-3/2

You know that the second line passes through (-6,5), so this tells us that x=-6, and y=5. Use y=mx+b, the equation of a line, to solve for b:

y=mx+b
5=(-3/2)(-6) + b
5 = 18/2 + b
5 = 9 + b
b = -4

The equation of the perpendicular line is y=(-3/2)x -4