SOLUTION: through (3,-2) perpendicular to 2x-y=5

Question 1200850: through (3,-2) perpendicular to 2x-y=5
Found 2 solutions by Alan3354, math_tutor2020:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
through (3,-2) perpendicular to 2x-y=5
----------------
Find the slope of the given line.
The slope of lines perpendicular is the negative inverse of the slope of the line.
----
Use y-y1 = m*(x-x1) where (x1,y1) is the given point and m is the slope.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: -x-2y = 1

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 -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.

Check out this lesson for another example
https://www.algebra.com/algebra/homework/Linear-equations/perpendicular-line-example1.lesson

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.

RELATED QUESTIONS
Line perpendicular to y=2x+3 and passes through (2,-3) (answered by Fombitz)
find the equation of the straight line passing through ((2/5),(3/7)) and perpendicular to (answered by Alan3354)
Write a linear equation that goes through (2, -3) and is perpendicular to y = 2x - 4. (answered by josgarithmetic)
Find the equation of the line. 1). Through (2,-1), parallel to y=3x-6 2).... (answered by josgarithmetic)
Find the equation of the line that passes through (2,-3) and is perpendicular to the line (answered by lwsshak3)
Find an equation of the line perpendicular to 2x-3y+3=0 and passing through... (answered by Cromlix)
I really need some help with this problem: write the slope/intercept form of the... (answered by MathLover1)
Find the distance between the point (3,5) and the line y= 3/2x + 5 given the slope of the (answered by josgarithmetic,ewatrrr)
what is perpendicular to y = -3x + 7, through (3,... (answered by mananth)