SOLUTION: For what value of a are the graphs of 6y=-2x+4 and 2y=ax-5perpendecular

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Question 1003061: For what value of a are the graphs of 6y=-2x+4 and 2y=ax-5perpendecular
Found 2 solutions by MathLover1, mananth:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the graphs of 6y=-2x%2B4 and 2y=ax-5 will be perpendicular if their slopes are negative reciprocals to each other
so, write first equations in the slope-intercept form
6y=-2x%2B4
y=-%282%2F6%29x%2B4%2F6
y=-%281%2F3%29x%2B2%2F3
as you can see, the slope is m=-%281%2F3%29
now to find the slope of the perpendicular line m%5Bp%5D, find negative reciprocal of m which will be m%5Bp%5D=-1%2Fm
plug in -%281%2F3%29 for m
m%5Bp%5D=-1%2F%28-1%2F3%29
m%5Bp%5D=3
so, your perpendicular line is:

2y=3x-5
see it on a graph:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%281%2F3%29x%2B2%2F3%2C3x%2F2-5%2F2%29+

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
6y=-2x+4 and 2y=ax-5perpendecular


6y=-2x+4
y=-2/6 x +2/3
y = (-1/3)x +2/3 slope = (-1/3)
2y=ax-5
y= (a/2)x -5/2 slope = (a/2)
For them to be perpendicular
(-1/3) = a/2
a= -2/3