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Question 1191902: A line passes through (2,4) and perpendicular to the line 3x+4y-4=0. Find the equation of the line.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Anything of the form Ax+By+C = 0 will have Bx-Ay+D = 0 perpendicular to it.
Note the swap of A and B, and also the sign change.
In the case of 3x+4y-4=0, we have
A = 3
B = 4
C = -4
So Bx-Ay+D = 0 becomes 4x-3y+D = 0
Plug in the coordinates of (x,y) = (2,4) and solve for D
4x-3y+D = 0
4(2)-3(4)+D = 0
8-12+D = 0
-4+D = 0
D = 4
We go from 4x-3y+D = 0 to 4x-3y+4 = 0 which is one way to write the equation of the perpendicular line. Other formats are possible.
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