SOLUTION: Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line. Perpendicular to the line -4x + 5y = -23; containin

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Question 979881: Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line.
Perpendicular to the line -4x + 5y = -23; containing the point (-3, 7)

I almost sure the answer is -5x + 4y = -13 but I dont know for sure
Thank you for your time
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
hi there,
Sort -4x + 5y = -23
into y = mx + c form
5y = 4x - 23
Divide through by 5
y = 4/5 - 23/5
Gradient = 4/5.
Lines that are perpendicular have
gradients that multiply together
to give -1
m1 x m2 = -1
Therefore the new line has a
gradient of -5/4 (4/5 x -5/4 = -1)
Using the coords -3,7 and the line
equation:
y - b = m(x - a)
y - 7 = -5/4(x - (-3))
y - 7 = -5/4(x + 3)
y - 7 = -5/4x -15/4
y = -5/4x - 15/4 + 28/4 (7)
y = -5/4x + 13/4
Multiply throughout by 4
4y = -5x + 13
5x + 4y = 13
Hope this helps:-)