SOLUTION: Choose an equation in slope-intercept form for the line that passes through (-12,3) and is perpendicular to the y= -(2/3)x-11.

Algebra ->  Geometry-proofs -> SOLUTION: Choose an equation in slope-intercept form for the line that passes through (-12,3) and is perpendicular to the y= -(2/3)x-11.      Log On


   

Question 976706: Choose an equation in slope-intercept form for the line that passes through (-12,3) and is perpendicular to the y= -(2/3)x-11.
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 -2%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%28-2%2F3%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%283%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=3%2F2 Multiply the fractions.


So the perpendicular slope is 3%2F2



So now we know the slope of the unknown line is 3%2F2 (its the negative reciprocal of -2%2F3 from the line y=%28-2%2F3%29%2Ax-11). Also since the unknown line goes through (-12,3), 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-3=%283%2F2%29%2A%28x%2B12%29 Plug in m=3%2F2, x%5B1%5D=-12, and y%5B1%5D=3



y-3=%283%2F2%29%2Ax-%283%2F2%29%28-12%29 Distribute 3%2F2



y-3=%283%2F2%29%2Ax%2B36%2F2 Multiply



y=%283%2F2%29%2Ax%2B36%2F2%2B3Add 3 to both sides to isolate y

y=%283%2F2%29%2Ax%2B36%2F2%2B6%2F2 Make into equivalent fractions with equal denominators



y=%283%2F2%29%2Ax%2B42%2F2 Combine the fractions



y=%283%2F2%29%2Ax%2B21 Reduce any fractions

So the equation of the line that is perpendicular to y=%28-2%2F3%29%2Ax-11 and goes through (-12,3) is y=%283%2F2%29%2Ax%2B21


So here are the graphs of the equations y=%28-2%2F3%29%2Ax-11 and y=%283%2F2%29%2Ax%2B21




graph of the given equation y=%28-2%2F3%29%2Ax-11 (red) and graph of the line y=%283%2F2%29%2Ax%2B21(green) that is perpendicular to the given graph and goes through (-12,3)