You can put this solution on YOUR website! through (3,-2) perpendicular to 2x-y=5
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Find the slope of the given line.
The slope of lines perpendicular is the negative inverse of the slope of the line.
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Use y-y1 = m*(x-x1) where (x1,y1) is the given point and m is the slope.
Anything perpendicular to Ax+By = C is of the form Bx-Ay = D.
I swapped the A and B, then negated one of them.
Compare 2x-y = 5 with Ax+By = C to find that
A = 2
B = -1
C = 5
This leads to Bx-Ay = D becoming -x-2y = D
Next plug in the coordinates of (x,y) = (3,-2) to compute D.
-x-2y = D
D = -x-2y
D = -3-2(-2)
D = -3+4
D = 1
We go from -x-2y = D to -x-2y = 1 which is the final answer. Other answers are possible.
You can use a graphing tool like GeoGebra or Desmos to confirm the answer is correct.
Optional Section:
If you were to solve for y, then you'll follow these steps.
-x-2y = 1
-2y = 1+x
-2y = x+1
y = (x+1)/(-2)
y = (-x/2) + (-1/2)
y = (-1/2)x - 1/2
This is in y = mx+b form with m = -1/2 as the slope and b = -1/2 as the y intercept.
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