SOLUTION: I need to write the equation of the line that is perpendicular to the given line and passes through the given point. I am stuck and confused. Here is the equation y=-3x+5 (-1,4

Algebra ->  Graphs -> SOLUTION: I need to write the equation of the line that is perpendicular to the given line and passes through the given point. I am stuck and confused. Here is the equation y=-3x+5 (-1,4      Log On


   

Question 122316: I need to write the equation of the line that is perpendicular to the given line and passes through the given point. I am stuck and confused.
Here is the equation
y=-3x+5 (-1,4)
y=mx+b
4=-3(-1)+b
4=3+b
4-3=3+b-3
1=b
y=1/3x+1
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%28-3%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-3%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%2B5). Also since the unknown line goes through (-1,4), 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-4=%281%2F3%29%2A%28x%2B1%29 Plug in m=1%2F3, x%5B1%5D=-1, and y%5B1%5D=4



y-4=%281%2F3%29%2Ax-%281%2F3%29%28-1%29 Distribute 1%2F3



y-4=%281%2F3%29%2Ax%2B1%2F3 Multiply



y=%281%2F3%29%2Ax%2B1%2F3%2B4Add 4 to both sides to isolate y

y=%281%2F3%29%2Ax%2B1%2F3%2B12%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B13%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B13%2F3 Reduce any fractions

So the equation of the line that is perpendicular to y=-3%2Ax%2B5 and goes through (-1,4) is y=%281%2F3%29%2Ax%2B13%2F3


So here are the graphs of the equations y=-3%2Ax%2B5 and y=%281%2F3%29%2Ax%2B13%2F3




graph of the given equation y=-3%2Ax%2B5 (red) and graph of the line y=%281%2F3%29%2Ax%2B13%2F3(green) that is perpendicular to the given graph and goes through (-1,4)