Expert: Lynn Houston - 12/11/2008

Question
i need to know how to write an equation for the line that is perpendicular to the given line and that passes through the given point.

i.e. y=-5x+9 and the given points are (-5,5)

Answer
The first thing you need to know is that perpendicular lines have inverse and opposite slopes.  So, the slope in the first eq is -5, so the slope of a line perpendicular to it has a slope of 1/5.  Now, take that slope and the given points and put it into the slope intercept eq (which is y = mx + b, where x is the slope and b is the y intercept) and solve for b.

5 = 1/5(-5) + b
5 = -1 + b
b = 6

Now you have the slope and the y intercept, so the eq of the line perpendicular to y = -5x+9 and passing through (-5,5) is
y = 1/5x + 6