Algebra Examples

Find the Perpendicular Line 4x-y=4 that contains the point (-2,-2)
that contains the point
Step 1
Solve .
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Dividing two negative values results in a positive value.
Step 1.2.2.2
Divide by .
Step 1.2.3
Simplify the right side.
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Step 1.2.3.1
Simplify each term.
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Step 1.2.3.1.1
Divide by .
Step 1.2.3.1.2
Move the negative one from the denominator of .
Step 1.2.3.1.3
Rewrite as .
Step 1.2.3.1.4
Multiply by .
Step 2
Find the slope when .
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Step 2.1
Rewrite in slope-intercept form.
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Step 2.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.1.2
Reorder and .
Step 2.2
Using the slope-intercept form, the slope is .
Step 3
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Step 4
Find the equation of the perpendicular line using the point-slope formula.
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Step 4.1
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 4.2
Simplify the equation and keep it in point-slope form.
Step 5
Write in form.
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Step 5.1
Solve for .
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Step 5.1.1
Simplify .
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Step 5.1.1.1
Rewrite.
Step 5.1.1.2
Simplify by adding zeros.
Step 5.1.1.3
Apply the distributive property.
Step 5.1.1.4
Combine and .
Step 5.1.1.5
Cancel the common factor of .
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Step 5.1.1.5.1
Move the leading negative in into the numerator.
Step 5.1.1.5.2
Factor out of .
Step 5.1.1.5.3
Cancel the common factor.
Step 5.1.1.5.4
Rewrite the expression.
Step 5.1.1.6
Move the negative in front of the fraction.
Step 5.1.2
Move all terms not containing to the right side of the equation.
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Step 5.1.2.1
Subtract from both sides of the equation.
Step 5.1.2.2
To write as a fraction with a common denominator, multiply by .
Step 5.1.2.3
Combine and .
Step 5.1.2.4
Combine the numerators over the common denominator.
Step 5.1.2.5
Simplify the numerator.
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Step 5.1.2.5.1
Multiply by .
Step 5.1.2.5.2
Subtract from .
Step 5.1.2.6
Move the negative in front of the fraction.
Step 5.2
Reorder terms.
Step 5.3
Remove parentheses.
Step 6