SOLUTION: Can you please help me solve this problem: Find the equation of the line which passes throught (3,-2) and is also perpendicular to the line y=3x+1. Thank you, I most appreciate

Algebra ->  Linear-equations -> SOLUTION: Can you please help me solve this problem: Find the equation of the line which passes throught (3,-2) and is also perpendicular to the line y=3x+1. Thank you, I most appreciate      Log On


   

Question 99826: Can you please help me solve this problem: Find the equation of the line which passes throught (3,-2) and is also perpendicular to the line y=3x+1.
Thank you, I most appreciate it
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B1). Also since the unknown line goes through (3,-2), 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%2B2=%28-1%2F3%29%2A%28x-3%29 Plug in m=-1%2F3, x%5B1%5D=3, and y%5B1%5D=-2



y%2B2=%28-1%2F3%29%2Ax%2B%281%2F3%29%283%29 Distribute -1%2F3



y%2B2=%28-1%2F3%29%2Ax%2B3%2F3 Multiply



y=%28-1%2F3%29%2Ax%2B3%2F3-2Subtract -2 from both sides to isolate y

y=%28-1%2F3%29%2Ax%2B3%2F3-6%2F3 Make into equivalent fractions with equal denominators



y=%28-1%2F3%29%2Ax-3%2F3 Combine the fractions



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

So the equation of the line that is perpendicular to y=3%2Ax%2B1 and goes through (3,-2) is y=%28-1%2F3%29%2Ax-1


So here are the graphs of the equations y=3%2Ax%2B1 and y=%28-1%2F3%29%2Ax-1




graph of the given equation y=3%2Ax%2B1 (red) and graph of the line y=%28-1%2F3%29%2Ax-1(green) that is perpendicular to the given graph and goes through (3,-2)