SOLUTION: Find the slope-intercept form of the equation that passes through the given point and is perpendicular to the given line. (-3,1) and y=-3x+7

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Question 1001262: Find the slope-intercept form of the equation that passes through the given point and is perpendicular to the given line.
(-3,1) and y=-3x+7
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 -3, 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%28-3%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-3%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%2F3 Multiply the fractions.


So the perpendicular slope is 1%2F3



So now we know the slope of the unknown line is 1%2F3 (its the negative reciprocal of -3 from the line y=-3%2Ax%2B7). Also since the unknown line goes through (-3,1), 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=%281%2F3%29%2A%28x%2B3%29 Plug in m=1%2F3, x%5B1%5D=-3, and y%5B1%5D=1



y-1=%281%2F3%29%2Ax-%281%2F3%29%28-3%29 Distribute 1%2F3



y-1=%281%2F3%29%2Ax%2B3%2F3 Multiply



y=%281%2F3%29%2Ax%2B3%2F3%2B1Add 1 to both sides to isolate y

y=%281%2F3%29%2Ax%2B3%2F3%2B3%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B6%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B2 Reduce any fractions

So the equation of the line that is perpendicular to y=-3%2Ax%2B7 and goes through (-3,1) is y=%281%2F3%29%2Ax%2B2


So here are the graphs of the equations y=-3%2Ax%2B7 and y=%281%2F3%29%2Ax%2B2




graph of the given equation y=-3%2Ax%2B7 (red) and graph of the line y=%281%2F3%29%2Ax%2B2(green) that is perpendicular to the given graph and goes through (-3,1)