SOLUTION: Write an equation of the line containing the given point and perpendicular to the given line. (7,-7);6x+5y=7 The equation of the line is y= ____

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: Write an equation of the line containing the given point and perpendicular to the given line. (7,-7);6x+5y=7 The equation of the line is y= ____      Log On

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Question 160014: Write an equation of the line containing the given point and perpendicular to the given line.
(7,-7);6x+5y=7
The equation of the line is y= ____
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Let's find the slope of the given line first.
Convert to slope-intercept form : y=mx%2Bb
6x%2B5y=7
5y=-6x%2B7
y=-%286%2F5%29x%2B7%2F5
The slope of the first line is m%5B1%5D=-%286%2F5%29.
Perpendicular lines have slopes that are negative reciprocals of each other.
m%5B1%5Dm%5B2%5D=-1
m%5B2%5D=5%2F6
Use the point-slope form of the line with slope, m%5B2%5D=5%2F6, and point (7,-7),
y-y%5B1%5D=m%28x-x%5B1%5D%29
y-%28-7%29=%285%2F6%29%28x-7%29
y%2B7=%285%2F6%29x-35%2F6
y=%285%2F6%29x-35%2F6-42%2F6
y=%285%2F6%29x-7%2F6
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Check the answer graphically.
drawing%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgrid%28+1+%29%2Ccircle%28+7%2C+-7%2C+.3+%29%2C+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-%286%2F5%29x%2B7%2F5%2C+%285%2F6%29x-7%2F6%29+%29