SOLUTION: If a graph is a line that is perpendicular to the line g(x)=5x-2 and contains the point (6,3), determine the linear function.

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Question 914725: If a graph is a line that is perpendicular to the line g(x)=5x-2 and contains the point (6,3), determine the linear function.
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 5, 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%285%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F5%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%2F5 Multiply the fractions.


So the perpendicular slope is -1%2F5



So now we know the slope of the unknown line is -1%2F5 (its the negative reciprocal of 5 from the line y=5%2Ax-2). Also since the unknown line goes through (6,3), 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=%28-1%2F5%29%2A%28x-6%29 Plug in m=-1%2F5, x%5B1%5D=6, and y%5B1%5D=3



y-3=%28-1%2F5%29%2Ax%2B%281%2F5%29%286%29 Distribute -1%2F5



y-3=%28-1%2F5%29%2Ax%2B6%2F5 Multiply



y=%28-1%2F5%29%2Ax%2B6%2F5%2B3Add 3 to both sides to isolate y

y=%28-1%2F5%29%2Ax%2B6%2F5%2B15%2F5 Make into equivalent fractions with equal denominators



y=%28-1%2F5%29%2Ax%2B21%2F5 Combine the fractions



y=%28-1%2F5%29%2Ax%2B21%2F5 Reduce any fractions

So the equation of the line that is perpendicular to y=5%2Ax-2 and goes through (6,3) is y=%28-1%2F5%29%2Ax%2B21%2F5


So here are the graphs of the equations y=5%2Ax-2 and y=%28-1%2F5%29%2Ax%2B21%2F5




graph of the given equation y=5%2Ax-2 (red) and graph of the line y=%28-1%2F5%29%2Ax%2B21%2F5(green) that is perpendicular to the given graph and goes through (6,3)