Algebra Examples

Find the Perpendicular Line What is an equation of the line that passes through the point (1,6) and is perpendicular to the line x+3y=27 ?
What is an equation of the line that passes through the point and is perpendicular to the line ?
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
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
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 in front of the fraction.
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 2.1.3
Write in form.
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Step 2.1.3.1
Reorder terms.
Step 2.1.3.2
Remove parentheses.
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
Cancel the common factor of and .
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Step 4.1.1
Rewrite as .
Step 4.1.2
Move the negative in front of the fraction.
Step 4.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.3
Multiply .
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Step 4.3.1
Multiply by .
Step 4.3.2
Multiply by .
Step 4.3.3
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
Solve for .
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Step 6.1
Simplify .
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Step 6.1.1
Rewrite.
Step 6.1.2
Simplify by adding zeros.
Step 6.1.3
Apply the distributive property.
Step 6.1.4
Multiply by .
Step 6.2
Move all terms not containing to the right side of the equation.
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Step 6.2.1
Add to both sides of the equation.
Step 6.2.2
Add and .
Step 7