SOLUTION: I HAVE A QUESTION ON WRITING EQUATIONS OF A LINE THAT PASSES THROUGH THE GIVEN POINT AND IS PERPENDICULAR TO THE GIVEN LINE. HERE IS THE PROBLEM: WRITE AN EQUATION OF A LINE TH

Algebra ->  Linear-equations -> SOLUTION: I HAVE A QUESTION ON WRITING EQUATIONS OF A LINE THAT PASSES THROUGH THE GIVEN POINT AND IS PERPENDICULAR TO THE GIVEN LINE. HERE IS THE PROBLEM: WRITE AN EQUATION OF A LINE TH      Log On


   

Question 174052: I HAVE A QUESTION ON WRITING EQUATIONS OF A LINE THAT PASSES THROUGH THE GIVEN POINT AND IS PERPENDICULAR TO THE GIVEN LINE.
HERE IS THE PROBLEM:
WRITE AN EQUATION OF A LINE THAT PASSES THROUGH THE GIVEN POINT AND IS PERPENDICULAR TO THE GIVEN LINE
(1,-1) Y= 3X+2
HOW DO I DO IT
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
The first thing you need to know is that the slopes of perpendicular lines have a product of -1.
y = mx +b. The slope of the given line is 3 (since the line is given as Y= 3X+2)
So the slope of the lines perpendicular to that line is -1/3
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 3, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%283%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F3%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-1%2F3 Multiply the fractions.


So the perpendicular slope is -1%2F3



So now we know the slope of the unknown line is -1%2F3 (its the negative reciprocal of 3 from the line y=3%2Ax%2B2). Also since the unknown line goes through (1,-1), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B1=%28-1%2F3%29%2A%28x-1%29 Plug in m=-1%2F3, x%5B1%5D=1, and y%5B1%5D=-1



y%2B1=%28-1%2F3%29%2Ax%2B%281%2F3%29%281%29 Distribute -1%2F3



y%2B1=%28-1%2F3%29%2Ax%2B1%2F3 Multiply



y=%28-1%2F3%29%2Ax%2B1%2F3-1Subtract -1 from both sides to isolate y

y=%28-1%2F3%29%2Ax%2B1%2F3-3%2F3 Make into equivalent fractions with equal denominators



y=%28-1%2F3%29%2Ax-2%2F3 Combine the fractions



y=%28-1%2F3%29%2Ax-2%2F3 Reduce any fractions

So the equation of the line that is perpendicular to y=3%2Ax%2B2 and goes through (1,-1) is y=%28-1%2F3%29%2Ax-2%2F3


So here are the graphs of the equations y=3%2Ax%2B2 and y=%28-1%2F3%29%2Ax-2%2F3




graph of the given equation y=3%2Ax%2B2 (red) and graph of the line y=%28-1%2F3%29%2Ax-2%2F3(green) that is perpendicular to the given graph and goes through (1,-1)