SOLUTION: What is the equation of the line in slope-intercept form? the line perpendicular to y = 1/3x + 5 through (2, 1)

Algebra ->  Trigonometry-basics -> SOLUTION: What is the equation of the line in slope-intercept form? the line perpendicular to y = 1/3x + 5 through (2, 1)      Log On


   

Question 739181: What is the equation of the line in slope-intercept form? the line perpendicular to
y = 1/3x + 5 through (2, 1)
Answer by MathLover1(20850) 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%281%2F3%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%283%2F1%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=%281%2F3%29%2Ax%2B5). Also since the unknown line goes through (2,1), 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-1=-3%2A%28x-2%29 Plug in m=-3, x%5B1%5D=2, and y%5B1%5D=1



y-1=-3%2Ax%2B%283%29%282%29 Distribute -3



y-1=-3%2Ax%2B6 Multiply



y=-3%2Ax%2B6%2B1Add 1 to both sides to isolate y

y=-3%2Ax%2B7 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F3%29%2Ax%2B5 and goes through (2,1) is y=-3%2Ax%2B7


So here are the graphs of the equations y=%281%2F3%29%2Ax%2B5 and y=-3%2Ax%2B7




graph of the given equation y=%281%2F3%29%2Ax%2B5 (red) and graph of the line y=-3%2Ax%2B7(green) that is perpendicular to the given graph and goes through (2,1)