# Algebra Examples

Find the Perpendicular Line
,
Use the slope-intercept form to find the slope.
The slope-intercept form is , where is the slope and is the y-intercept.
Using the slope-intercept form, the slope is .
The equation of a perpendicular line to must have a slope that is the negative reciprocal of the original slope.
Simplify to find the slope of the perpendicular line.
Move the negative in front of the fraction.
Simplify .
Multiply by to get .
Multiply by to get .
Find the equation of the perpendicular line using the point-slope formula.
Find the value of using the formula for the equation of a line.
Use the formula for the equation of a line to find .
Substitute the value of into the equation.
Substitute the value of into the equation.
Substitute the value of into the equation.
Find the value of .
Rewrite the equation as .
Simplify each term.
Multiply by to get .
Simplify .
Write as a fraction with denominator .
Multiply and to get .
Move the negative in front of the fraction.
Move all terms not containing to the right side of the equation.
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Simplify the right side of the equation.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by to get .
Subtract from to get .
Move the negative in front of the fraction.
Now that the values of (slope) and (y-intercept) are known, substitute them into to find the equation of the line.

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