SOLUTION: Find the equation of a perpendicular line to 7x + 8y - 12 = 0 and passing through (-2, 5). Write the answer in standard form.

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Question 1181494: Find the equation of a perpendicular line to 7x + 8y - 12 = 0 and passing
through (-2, 5). Write the answer in standard form.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Write the standard form equation of the line that is perpendicular to
7x+%2B+8y+-+12+=+0 and passes through (-2, 5).
first write 7x+%2B+8y+-+12+=+0 in slope intercept form
+8y++=+-7x%2B12+
y=-%287%2F8%29x%2B12%2F8+
y=-%287%2F8%29x%2B3%2F2+=> a slope is m=-%287%2F8%29
the line that is perpendicular to given line is negative reciprocal to m=-%287%2F8%29
m%5Bp%5D=-1%2F%28-7%2F8%29
m%5Bp%5D=8%2F7

use slope point formula to find equation of the line that is perpendicular to given line
y-y%5B1%5D=m%5Bp%5D%28x-x%5B1%5D%29........substitute a slope, and coordinates of given point (-2, 5)

y-5=%288%2F7%29%28x-%28-2%29%29
y-5=%288%2F7%29%28x%2B2%29
y-5=%288%2F7%29x%2B16%2F7
y=%288%2F7%29x%2B16%2F7%2B5
y=%288%2F7%29x%2B51%2F7-> write it in standard form ax%2Bby=c, both sides multiply by 7
7y=8x%2B51
-8x%2B7y-51=0