Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula:
where is the perpendicular slope
So plug in the given slope to find the perpendicular slope
When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second
Multiply the fractions.
So the perpendicular slope is
So now we know the slope of the unknown line is (its the negative reciprocal of from the line ).
Also since the unknown line goes through (5,3), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
where m is the slope and (,) is the given point
Plug in , , and
Distribute
Multiply
Add to both sides to isolate y
Make into equivalent fractions with equal denominators
Combine the fractions
Reduce any fractions
So the equation of the line that is perpendicular to and goes through (,) is
So here are the graphs of the equations and
graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)
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