SOLUTION: Find an equation for the linear function g(x) which is perpendicular to the line 7x−4y=8 and intersects the line 7x−4y=8 at x=24.

Algebra ->  Linear-equations -> SOLUTION: Find an equation for the linear function g(x) which is perpendicular to the line 7x−4y=8 and intersects the line 7x−4y=8 at x=24.      Log On


   

Question 345409: Find an equation for the linear function g(x) which is perpendicular to the line 7x−4y=8 and intersects the line 7x−4y=8 at x=24.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the intersection point.
+7x-4y=8
7%2824%29-4y=8
168-4y=8
-4y=-160
y=40
(24,40)
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Now find the perpendicular line,
7x-4y=8
-4y=-7x%2B8
y=%287%2F4%29x-2
Perpendicular lines have slopes that are negative reciprocals,
m1%2Am2=-1
%287%2F4%29%2Am2=-1
m2=-4%2F7
Use the point-slope form of a line, y=mx%2Bb
y=-%284%2F7%29x%2Bb
USe the point (24,40) to solve for b.
40=-%284%2F7%29%2824%29%2Bb
b=280%2F7%2B96%2F7
b=376%2F7
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highlight%28y=-%284%2F7%29x%2B376%2F7%29
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