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Question 826787: Find an equation of the line that passes through the given point and is perpendicular to the given line. Write the equation in slope-intercept form.
(8, −4), 5x = 7y − 8
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Find an equation of the line that passes through the given point and is perpendicular to the given line. Write the equation in slope-intercept form.
(8, −4), 5x = 7y − 8
.
First, find slope of:
5x = 7y − 8
5x+8 = 7y
(5/7)x+8/7 = y
slope is 5/7
.
slope of "perpendicular" is negative reciprocal of 5/7:
slope of new line then is
-7/5
.
using slope (-7/5) and (8,-4)
plug into "point-slope" form:
y - y1 = m(x - x1)
y - (-4) = (-7/5)(x - 8)
y + 4 = (-7/5)(x - 8)
y + 4 = (-7/5)x - (-7/5)8
y + 4 = (-7/5)x + 56/5
y = (-7/5)x + 56/5 - 4
y = (-7/5)x + 56/5 - 20/5
y = (-7/5)x + (56-20)/5
y = (-7/5)x + 36/5
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