Algebra Examples

Find Any Equation Perpendicular to the Line
Choose a point that the perpendicular line will pass through.
Solve .
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Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Find the slope when .
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Rewrite in slope-intercept form.
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The slope-intercept form is , where is the slope and is the y-intercept.
Reorder and .
Rewrite in slope-intercept form.
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.
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Multiply the numerator by the reciprocal of the denominator.
Multiply by to get .
Find the equation of the perpendicular line using the point-slope formula.
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Find the value of using the formula for the equation of a line.
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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 .
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Rewrite the equation as .
Simplify the left side.
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Simplify each term.
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Multiply by to get .
Simplify .
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Multiply by to get .
Multiply by to get .
Add and to get .
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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