Finite Math Examples

Find Any Equation Perpendicular to the Line y-(-12)=-1/2*(x-(-6))
Step 1
Choose a point that the perpendicular line will pass through.
Step 2
Solve .
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Step 2.1
Multiply by .
Step 2.2
Simplify .
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Step 2.2.1
Multiply by .
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Combine and .
Step 2.2.4
Cancel the common factor of .
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Step 2.2.4.1
Move the leading negative in into the numerator.
Step 2.2.4.2
Factor out of .
Step 2.2.4.3
Cancel the common factor.
Step 2.2.4.4
Rewrite the expression.
Step 2.2.5
Multiply by .
Step 2.3
Move all terms not containing to the right side of the equation.
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Step 2.3.1
Subtract from both sides of the equation.
Step 2.3.2
Subtract from .
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
Write in form.
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Step 3.1.2.1
Reorder terms.
Step 3.1.2.2
Remove parentheses.
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
Cancel the common factor of and .
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Step 5.1.1
Rewrite as .
Step 5.1.2
Move the negative in front of the fraction.
Step 5.2
Multiply the numerator by the reciprocal of the denominator.
Step 5.3
Multiply .
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Step 5.3.1
Multiply by .
Step 5.3.2
Multiply by .
Step 5.3.3
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
Solve for .
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Step 7.1
Add and .
Step 7.2
Add and .
Step 8