SOLUTION: I need help figuring out this question we have to find the equation- Contains to (-3,5) and is perpendicular to 2x+3y=7

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Question 1049391: I need help figuring out this question we have to find the equation- Contains to (-3,5) and is perpendicular to 2x+3y=7
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the slope of your original line.
2x%2B3y=7
3y=-2x%2B7
y=-%282%2F3%29x%2B7%2F3
m%5B1%5D=-2%2F3
Perpendicular lines have slopes that are negative reciprocals,
m%5B1%5Dm%5B2%5D=-1
-%282%2F3%29m%5B2%5D=-1
m%5B2%5D=3%2F2
So then use the point slope form with this slope and the point,
y-5=%283%2F2%29%28x-%28-3%29%29
2y-10=3%28x%2B3%29
2y-10=3x%2B9
-3x%2B2y=19
3x-2y=-19
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Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
2x +3y = 7
:
3y = -2x + 7
:
1) y = -2x/3 + 7/3
:
The line perpendicular to line 1) has a slope = the negative reciprocal of line 1)'s slope
:
slope(m) of line 1) = -2/3
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therefore the slope of the perpendicular line is -(-3/2) = (3/2)
:
so far we have
:
y = 3x/2 + b, where b is the y intercept
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use the given point (-3, 5)
:
5 = 3(-3)/2 + b
:
5 = -9/2 + b
:
b = (10/2) + (9/2) = 9.5
:
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y = 3x/2 +9.5 is equivalent to
:
2y -3x = 19
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