SOLUTION: Find the equation for the line that passes through the point (-1,-3), and that is perpendicular to the line with the equation y=-1/3x+1. Slope: m1= -1/3 Slope: m2= 3 Y-(-3)= 3(x

Algebra ->  Linear-equations -> SOLUTION: Find the equation for the line that passes through the point (-1,-3), and that is perpendicular to the line with the equation y=-1/3x+1. Slope: m1= -1/3 Slope: m2= 3 Y-(-3)= 3(x      Log On


   

Question 990932: Find the equation for the line that passes through the point (-1,-3), and that is perpendicular to the line with the equation y=-1/3x+1.
Slope: m1= -1/3
Slope: m2= 3
Y-(-3)= 3(x-(-1))
3(y-(-3)) =3(x-(-1))
3y-9= 3x-3
3x-3y= 6
Y= 3x+6
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure why you did step 2. It is an incorrect algebraic move.

Here's how you do the problem

y-(-3)= 3(x-(-1)) ... you had step 1 correct
y+3 = 3(x+1)
y+3 = 3x+3
y+3-3 = 3x+3-3 ... Subtract 3 from both sides.
y = 3x

So the final answer is y = 3x

Answer by MathLover1(20849) 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 -1%2F3, 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%28-1%2F3%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%283%2F-1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=3%2F1 Multiply the fractions.


So the perpendicular slope is 3



So now we know the slope of the unknown line is 3 (its the negative reciprocal of -1%2F3 from the line y=%28-1%2F3%29%2Ax%2B1). Also since the unknown line goes through (-1,-3), 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%2B3=3%2A%28x%2B1%29 Plug in m=3, x%5B1%5D=-1, and y%5B1%5D=-3



y%2B3=3%2Ax-%283%29%28-1%29 Distribute 3



y%2B3=3%2Ax%2B3 Multiply



y=3%2Ax%2B3-3Subtract -3 from both sides to isolate y

y=3%2Ax%2B0 Combine like terms

So the equation of the line that is perpendicular to y=%28-1%2F3%29%2Ax%2B1 and goes through (-1,-3) is y=3%2Ax%2B0


So here are the graphs of the equations y=%28-1%2F3%29%2Ax%2B1 and y=3%2Ax%2B0




graph of the given equation y=%28-1%2F3%29%2Ax%2B1 (red) and graph of the line y=3%2Ax%2B0(green) that is perpendicular to the given graph and goes through (-1,-3)