Question 1200850
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Answer: <font color=red>-x-2y = 1</font>


Explanation:


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 <font color=red>-x-2y = 1</font> 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.


Check out this lesson for another example
<a href = "https://www.algebra.com/algebra/homework/Linear-equations/perpendicular-line-example1.lesson">https://www.algebra.com/algebra/homework/Linear-equations/perpendicular-line-example1.lesson</a>



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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