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Start with the given equation.
Subtract 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 to get . 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
Plug in and
Multiply both sides by 3 to clear the fraction
Subtract 3 from both sides. Add 4x to both sides.
Combine like terms.
So the equation of the line perpendicular to that goes through the point in standard form is .