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Question 977558: Given a line with equation 6x-y=5. Write an equation in point-slope form of the line perpendicular to the given line through the point (2, -3).
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
First sort your equation into y = mx + c
6x - y = 5 => y = 6x - 5
Gradient = 6
Lines that are perpendicular to one another
have gradients that multiply together to give -1
m(1) x m(2) = -1
So, 6 x m(2) = -1
m(2) = -1/6
Now substitute this gradient into the line equation
y - b = m(x - a)
y - b = -1/6(x - a)
Substitute coordinates (2, -3)
y - (-3) = -1/6(x - 2)
y + 3 = -1/6x + 1/3
y = -1/6x + 1/3 - 9/3 (3 = 9/3)
y = -1/6x - 8/3
Multiply through by 12
12y = -2x - 24
Hope this helps:-)
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