SOLUTION: Find an equation for the line perpendicular to the line 4x + 20y = 6 having the same y-intercept as −5x − 7y = 56

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Question 1076932: Find an equation for the line perpendicular to the line 4x + 20y = 6 having the same y-intercept as −5x − 7y = 56
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find an equation for the line perpendicular to the line 4x+%2B+20y+=+6+
equation of the perpendicular line:
y=mx%2Bb
if given that the line perpendicular to the line 4x+%2B+20y+=+6+, means they will have slopes negative reciprocal to each other
so, first find a slope of given line:
4x+%2B+20y+=+6+
+20y+=+-4x%2B6+
+y+=+-%284%2F20%29x%2B6%2F20+
+y+=+-%281%2F5%29x%2B3%2F10+=> slope is m=-%281%2F5%29
and its negative reciprocal will be a slope of the perpendicular line:
if m=-%281%2F5%29, than negative reciprocal is -1%2F%28-%281%2F5%29%29=>5
now we have a slope, and your equation is y=5x%2Bb so far
since given that perpendicular line having the same y-intercept as -5x+-+7y+=+56+, we need to find that y-intercept
-5x-56+=+7y+
y=-%285%2F7%29x+-+56%2F7+
y=-%285%2F7%29x+-8+=> y-intercept is at b=+-8
so, your equation is:y=5x-8

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+5x-8%2C+-%281%2F5%29x%2B3%2F10%29+