Expert: Lynn Houston - 12/12/2008

Question
Find the equation of the line , in slope-intercept form , perpendicular to y=2x+3 passing through point(4,-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 2, so the slope of a line perpendicular to it has a slope of -1/2.  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 = -1/2(4) + b
5 = -2 + b
b = 7

Now you have the slope and the y intercept, so the eq of the line perpendicular to y=2x+3 passing through point(4,-5) is
y = -1/2x + 7