SOLUTION: write an equation of the line containing the given point perpendicular to the given line. Express your answer in the form y=mx+b. (3,6);6x+y=8

Algebra ->  Linear-equations -> SOLUTION: write an equation of the line containing the given point perpendicular to the given line. Express your answer in the form y=mx+b. (3,6);6x+y=8      Log On


   

Question 275021: write an equation of the line containing the given point perpendicular to the given line. Express your answer in the form y=mx+b. (3,6);6x+y=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First solve for y to get y=-6x%2B8

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 -6, 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%28-6%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-6%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%2F6 Multiply the fractions.


So the perpendicular slope is 1%2F6



So now we know the slope of the unknown line is 1%2F6 (its the negative reciprocal of -6 from the line y=-6%2Ax%2B8). Also since the unknown line goes through (3,6), 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-6=%281%2F6%29%2A%28x-3%29 Plug in m=1%2F6, x%5B1%5D=3, and y%5B1%5D=6



y-6=%281%2F6%29%2Ax-%281%2F6%29%283%29 Distribute 1%2F6



y-6=%281%2F6%29%2Ax-3%2F6 Multiply



y=%281%2F6%29%2Ax-3%2F6%2B6Add 6 to both sides to isolate y

y=%281%2F6%29%2Ax-3%2F6%2B36%2F6 Make into equivalent fractions with equal denominators



y=%281%2F6%29%2Ax%2B33%2F6 Combine the fractions



y=%281%2F6%29%2Ax%2B11%2F2 Reduce any fractions

So the equation of the line that is perpendicular to y=-6%2Ax%2B8 and goes through (3,6) is y=%281%2F6%29%2Ax%2B11%2F2


So here are the graphs of the equations y=-6%2Ax%2B8 and y=%281%2F6%29%2Ax%2B11%2F2




graph of the given equation y=-6%2Ax%2B8 (red) and graph of the line y=%281%2F6%29%2Ax%2B11%2F2(green) that is perpendicular to the given graph and goes through (3,6)