SOLUTION: What is an equation of the line through the point (-6,6) and perpendicular to -5x-4y=6

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Question 188058: What is an equation of the line through the point (-6,6) and perpendicular
to -5x-4y=6
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We'll see the Slope of line -5x-4y=6 via Slope-Intercept Form, y=mx%2Bb:
Arranging the variables,
4y=-5x-6, divide by 4
y=%28-5x-6%29%2F4===> y=%28-5%2F4%29x-%286%2F4%29 ===>y=highlight%28%28-5%2F4%29%29x-3%2F2
It's Slope=m1= -5/4

*Remember, for perpendicular lines, m%5B2%5D=-1%2Fm%5B1%5D=%28-1%29%2F%28-5%2F4%29=%28-1%29%28-4%2F5%29=red%284%2F5%29

The, line passing thru point (-6,6) has slope=m2=4/5, and via Slope-Intercept Form:
6=%284%2F5%29%28-6%29%2Bb
6=-24%2F5%2Bb ----> b=6%2B24%2F5=%2830%2B24%29%2F5=54%2F5 Y-Intercept
The Line Eqn follows===> y=(4/5)x+(54/5), Or in Standard From, (-4/5)x+y=54/5. Remove fraction by multiplying the eqn by "5":
-4x+5y=54 , Answer

Thank you,
Jojo