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Is the equation supposed to be
. I'll assume that it is.
Start with the given equation.
from both sides.
Rearrange the terms.
Divide both sides by
to isolate y.
Break up the fraction.
We can see that the equation
has a slope
and a y-intercept
Now to find the slope of the perpendicular line, simply flip the slope
. Now change the sign to get
. So the perpendicular slope is
Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope
and the coordinates of the given point
Start with the point slope formula
Add 9 to both sides.
Combine like terms. note: If you need help with fractions, check out this solver
So the equation of the line perpendicular to
that goes through the point
Here's a graph to visually verify our answer:
Graph of the original equation
(red) and the perpendicular line
(green) through the point