SOLUTION: find an equation for the line perpendicular to the line -4x-8y=3 having the same Y-intercept as 6x-4y=-6

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Question 658972: find an equation for the line perpendicular to the line -4x-8y=3 having the same Y-intercept as 6x-4y=-6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Since slopes of perpendicular lines are negative reciprocals of each other,
first find a slope of the line -4x-8y=3
use the slope-intercept form y=mx%2Bb where m is a slope and b is y-intercept

-4x-3=8y

-%284%2F8%29x-3%2F8=y

y=-%281%2F2%29x-3%2F8.....as you can see m=-%281%2F2%29 and b=-3%2F8
now, let y=m%5B1%5Dx%2Bb%5B1%5D be a line that is perpendicular on given line

if m=-%281%2F2%29, then negative reciprocals of it is m%5B1%5D=-%281%2F%28-1%2F2%29%29
highlight%28m%5B1%5D=2%29
since given that new line has the same y-intercept as 6x-4y=-6, means b%5B1%5D will be:
6x-4y=-6...first solve for y
6x%2B6=4y
6x%2F4%2B6%2F4=y
y=%283%2F2%29x%2B3%2F2....=>...highlight%28b%5B1%5D=3%2F2%29
now, our line is:
highlight%28y=2x%2B3%2F2%29
let's see our line on a graph:

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%29+

now, check if this line is perpendicular to -4x-3=8y:

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%2C-%281%2F2%29x-3%2F8%29+

now check if our line has same y-intercept as 6x-4y=-6:

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%2C%283%2F2%29x%2B3%2F2%29+