Algebra Examples

Find the Perpendicular Line A line is perpendicular to y=-1/5x+1 and intersects the point (-5,1) What is the equation of this perpendicular line?
A line is perpendicular to and intersects the point What is the equation of this perpendicular line?
Step 1
Find the slope when .
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Step 1.1
Rewrite in slope-intercept form.
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Step 1.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 1.1.2
Simplify the right side.
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Step 1.1.2.1
Combine and .
Step 1.1.3
Write in form.
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Step 1.1.3.1
Reorder terms.
Step 1.1.3.2
Remove parentheses.
Step 1.2
Using the slope-intercept form, the slope is .
Step 2
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Step 3
Simplify to find the slope of the perpendicular line.
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Step 3.1
Cancel the common factor of and .
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Step 3.1.1
Rewrite as .
Step 3.1.2
Move the negative in front of the fraction.
Step 3.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.3
Multiply .
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Step 3.3.1
Multiply by .
Step 3.3.2
Multiply by .
Step 3.3.3
Multiply by .
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
Solve for .
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Step 5.1
Simplify .
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Step 5.1.1
Rewrite.
Step 5.1.2
Simplify by adding zeros.
Step 5.1.3
Apply the distributive property.
Step 5.1.4
Multiply by .
Step 5.2
Move all terms not containing to the right side of the equation.
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Step 5.2.1
Add to both sides of the equation.
Step 5.2.2
Add and .
Step 6