SOLUTION: What is an equation of the line perpendicular to the graph of y = -2x + 5 that passes through the point at (4, 7)? Write your answer in slope intercept form.

Algebra ->  Linear-equations -> SOLUTION: What is an equation of the line perpendicular to the graph of y = -2x + 5 that passes through the point at (4, 7)? Write your answer in slope intercept form.      Log On


   

Question 478245: What is an equation of the line perpendicular to the graph of y = -2x + 5 that passes through the point at (4, 7)? Write your answer in slope intercept form.
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 -2, 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%28-2%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-2%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%2F2 Multiply the fractions.


So the perpendicular slope is 1%2F2



So now we know the slope of the unknown line is 1%2F2 (its the negative reciprocal of -2 from the line y=-2%2Ax%2B5). Also since the unknown line goes through (4,7), 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-7=%281%2F2%29%2A%28x-4%29 Plug in m=1%2F2, x%5B1%5D=4, and y%5B1%5D=7



y-7=%281%2F2%29%2Ax-%281%2F2%29%284%29 Distribute 1%2F2



y-7=%281%2F2%29%2Ax-4%2F2 Multiply



y=%281%2F2%29%2Ax-4%2F2%2B7Add 7 to both sides to isolate y

y=%281%2F2%29%2Ax-4%2F2%2B14%2F2 Make into equivalent fractions with equal denominators



y=%281%2F2%29%2Ax%2B10%2F2 Combine the fractions



y=%281%2F2%29%2Ax%2B5 Reduce any fractions

So the equation of the line that is perpendicular to y=-2%2Ax%2B5 and goes through (4,7) is y=%281%2F2%29%2Ax%2B5


So here are the graphs of the equations y=-2%2Ax%2B5 and y=%281%2F2%29%2Ax%2B5




graph of the given equation y=-2%2Ax%2B5 (red) and graph of the line y=%281%2F2%29%2Ax%2B5(green) that is perpendicular to the given graph and goes through (4,7)