SOLUTION: Find an equation of the line perpendicular to 9x+4y=6 and containing the point (1, -1). Answer in slope intercept form. Thanks for your help.

Algebra ->  Equations -> SOLUTION: Find an equation of the line perpendicular to 9x+4y=6 and containing the point (1, -1). Answer in slope intercept form. Thanks for your help.      Log On


   

Question 923707: Find an equation of the line perpendicular to 9x+4y=6 and containing the point (1, -1). Answer in slope intercept form. Thanks for your help.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
an equation of the line perpendicular to 9x%2B4y=6 and containing the point (1, -1):
4y=-9x%2B6
y=-%289%2F4%29x%2B6%2F4
y=-%289%2F4%29x%2B3%2F2

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 -9%2F4, 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%28-9%2F4%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%284%2F-9%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=4%2F9 Multiply the fractions.


So the perpendicular slope is 4%2F9



So now we know the slope of the unknown line is 4%2F9 (its the negative reciprocal of -9%2F4 from the line y=%28-9%2F4%29%2Ax%2B3%2F2). Also since the unknown line goes through (1,-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%2B1=%284%2F9%29%2A%28x-1%29 Plug in m=4%2F9, x%5B1%5D=1, and y%5B1%5D=-1



y%2B1=%284%2F9%29%2Ax-%284%2F9%29%281%29 Distribute 4%2F9



y%2B1=%284%2F9%29%2Ax-4%2F9 Multiply



y=%284%2F9%29%2Ax-4%2F9-1Subtract -1 from both sides to isolate y

y=%284%2F9%29%2Ax-4%2F9-9%2F9 Make into equivalent fractions with equal denominators



y=%284%2F9%29%2Ax-13%2F9 Combine the fractions



y=%284%2F9%29%2Ax-13%2F9 Reduce any fractions

So the equation of the line that is perpendicular to y=%28-9%2F4%29%2Ax%2B3%2F2 and goes through (1,-1) is y=%284%2F9%29%2Ax-13%2F9


So here are the graphs of the equations y=%28-9%2F4%29%2Ax%2B3%2F2 and y=%284%2F9%29%2Ax-13%2F9




graph of the given equation y=%28-9%2F4%29%2Ax%2B3%2F2 (red) and graph of the line y=%284%2F9%29%2Ax-13%2F9(green) that is perpendicular to the given graph and goes through (1,-1)