Algebra Examples

Find the Perpendicular Line Find the equation of a line perpendicular to 4x-5y=-1 that contains the point (5,-4)
Find the equation of a line perpendicular to that contains the point
Step 1
Write the problem as a mathematical expression.
,
Step 2
Solve .
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Simplify each term.
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Step 2.2.3.1.1
Dividing two negative values results in a positive value.
Step 2.2.3.1.2
Dividing two negative values results in a positive value.
Step 3
Find the slope when .
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Step 3.1
Rewrite in slope-intercept form.
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Step 3.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 3.1.2
Reorder and .
Step 3.1.3
Reorder terms.
Step 3.2
Using the slope-intercept form, the slope is .
Step 4
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Step 5
Simplify to find the slope of the perpendicular line.
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Step 5.1
Multiply the numerator by the reciprocal of the denominator.
Step 5.2
Multiply by .
Step 6
Find the equation of the perpendicular line using the point-slope formula.
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Step 6.1
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 6.2
Simplify the equation and keep it in point-slope form.
Step 7
Write in form.
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Step 7.1
Solve for .
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Step 7.1.1
Simplify .
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Step 7.1.1.1
Rewrite.
Step 7.1.1.2
Simplify by adding zeros.
Step 7.1.1.3
Apply the distributive property.
Step 7.1.1.4
Combine and .
Step 7.1.1.5
Multiply .
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Step 7.1.1.5.1
Multiply by .
Step 7.1.1.5.2
Combine and .
Step 7.1.1.5.3
Multiply by .
Step 7.1.1.6
Move to the left of .
Step 7.1.2
Move all terms not containing to the right side of the equation.
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Step 7.1.2.1
Subtract from both sides of the equation.
Step 7.1.2.2
To write as a fraction with a common denominator, multiply by .
Step 7.1.2.3
Combine and .
Step 7.1.2.4
Combine the numerators over the common denominator.
Step 7.1.2.5
Simplify the numerator.
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Step 7.1.2.5.1
Multiply by .
Step 7.1.2.5.2
Subtract from .
Step 7.2
Reorder terms.
Step 7.3
Remove parentheses.
Step 8