Algebra Examples

Find the Perpendicular Line (3x-3y)/3=(x-3)/6 , (11,12)
,
Step 1
Solve .
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Step 1.1
Cancel the common factor of and .
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Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.1.4
Cancel the common factors.
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Step 1.1.4.1
Factor out of .
Step 1.1.4.2
Cancel the common factor.
Step 1.1.4.3
Rewrite the expression.
Step 1.1.4.4
Divide by .
Step 1.2
Solve for .
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Step 1.2.1
Move all terms not containing to the right side of the equation.
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Step 1.2.1.1
Subtract from both sides of the equation.
Step 1.2.1.2
Simplify each term.
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Step 1.2.1.2.1
Split the fraction into two fractions.
Step 1.2.1.2.2
Simplify each term.
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Step 1.2.1.2.2.1
Cancel the common factor of and .
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Step 1.2.1.2.2.1.1
Factor out of .
Step 1.2.1.2.2.1.2
Cancel the common factors.
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Step 1.2.1.2.2.1.2.1
Factor out of .
Step 1.2.1.2.2.1.2.2
Cancel the common factor.
Step 1.2.1.2.2.1.2.3
Rewrite the expression.
Step 1.2.1.2.2.2
Move the negative in front of the fraction.
Step 1.2.2
Divide each term in by and simplify.
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Step 1.2.2.1
Divide each term in by .
Step 1.2.2.2
Simplify the left side.
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Step 1.2.2.2.1
Dividing two negative values results in a positive value.
Step 1.2.2.2.2
Divide by .
Step 1.2.2.3
Simplify the right side.
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Step 1.2.2.3.1
Combine the numerators over the common denominator.
Step 1.2.2.3.2
To write as a fraction with a common denominator, multiply by .
Step 1.2.2.3.3
Simplify terms.
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Step 1.2.2.3.3.1
Combine and .
Step 1.2.2.3.3.2
Combine the numerators over the common denominator.
Step 1.2.2.3.4
Simplify each term.
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Step 1.2.2.3.4.1
Simplify the numerator.
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Step 1.2.2.3.4.1.1
Factor out of .
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Step 1.2.2.3.4.1.1.1
Raise to the power of .
Step 1.2.2.3.4.1.1.2
Factor out of .
Step 1.2.2.3.4.1.1.3
Factor out of .
Step 1.2.2.3.4.1.1.4
Factor out of .
Step 1.2.2.3.4.1.2
Multiply by .
Step 1.2.2.3.4.1.3
Subtract from .
Step 1.2.2.3.4.2
Move to the left of .
Step 1.2.2.3.4.3
Move the negative in front of the fraction.
Step 1.2.2.3.5
Simplify by multiplying through.
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Step 1.2.2.3.5.1
Move the negative one from the denominator of .
Step 1.2.2.3.5.2
Rewrite as .
Step 1.2.2.3.5.3
Apply the distributive property.
Step 1.2.2.3.6
Multiply .
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Step 1.2.2.3.6.1
Multiply by .
Step 1.2.2.3.6.2
Multiply by .
Step 1.2.2.3.7
Multiply .
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Step 1.2.2.3.7.1
Multiply by .
Step 1.2.2.3.7.2
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 terms.
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
Simplify to find the slope of the perpendicular line.
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Step 4.1
Multiply the numerator by the reciprocal of the denominator.
Step 4.2
Multiply by .
Step 5
Find the equation of the perpendicular line using the point-slope formula.
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Step 5.1
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 5.2
Simplify the equation and keep it in point-slope form.
Step 6
Write in form.
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Step 6.1
Solve for .
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Step 6.1.1
Simplify .
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Step 6.1.1.1
Rewrite.
Step 6.1.1.2
Simplify by adding zeros.
Step 6.1.1.3
Apply the distributive property.
Step 6.1.1.4
Combine and .
Step 6.1.1.5
Multiply .
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Step 6.1.1.5.1
Multiply by .
Step 6.1.1.5.2
Combine and .
Step 6.1.1.5.3
Multiply by .
Step 6.1.1.6
Move to the left of .
Step 6.1.2
Move all terms not containing to the right side of the equation.
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Step 6.1.2.1
Add to both sides of the equation.
Step 6.1.2.2
To write as a fraction with a common denominator, multiply by .
Step 6.1.2.3
Combine and .
Step 6.1.2.4
Combine the numerators over the common denominator.
Step 6.1.2.5
Simplify the numerator.
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Step 6.1.2.5.1
Multiply by .
Step 6.1.2.5.2
Add and .
Step 6.2
Reorder terms.
Step 6.3
Remove parentheses.
Step 7