SOLUTION: write and equation of a line that goes through (-3,13) and is perpendicular to 9x+4y=48

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Question 784337: write and equation of a line that goes through (-3,13) and is perpendicular to 9x+4y=48
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
equation of a line that goes through (-3,13) and is perpendicular to
9x%2B4y=48 ....solve for y
4y=-9x%2B48
y=-%289%2F4%29x%2B48%2F4
y=-%289%2F4%29x%2B12

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%2B12). Also since the unknown line goes through (-3,13), 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-13=%284%2F9%29%2A%28x%2B3%29 Plug in m=4%2F9, x%5B1%5D=-3, and y%5B1%5D=13



y-13=%284%2F9%29%2Ax-%284%2F9%29%28-3%29 Distribute 4%2F9



y-13=%284%2F9%29%2Ax%2B12%2F9 Multiply



y=%284%2F9%29%2Ax%2B12%2F9%2B13Add 13 to both sides to isolate y

y=%284%2F9%29%2Ax%2B12%2F9%2B117%2F9 Make into equivalent fractions with equal denominators



y=%284%2F9%29%2Ax%2B129%2F9 Combine the fractions



y=%284%2F9%29%2Ax%2B43%2F3 Reduce any fractions

So the equation of the line that is perpendicular to y=%28-9%2F4%29%2Ax%2B12 and goes through (-3,13) is y=%284%2F9%29%2Ax%2B43%2F3


So here are the graphs of the equations y=%28-9%2F4%29%2Ax%2B12 and y=%284%2F9%29%2Ax%2B43%2F3




graph of the given equation y=%28-9%2F4%29%2Ax%2B12 (red) and graph of the line y=%284%2F9%29%2Ax%2B43%2F3(green) that is perpendicular to the given graph and goes through (-3,13)