Algebra Examples

Find the Perpendicular Line passing through (-2,8) and perpendicular to y=2x+5
passing through and perpendicular to
Step 1
Use the slope-intercept form to find the slope.
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Step 1.1
The slope-intercept form is , where is the slope and is the y-intercept.
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
Find the equation of the perpendicular line using the point-slope formula.
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Step 3.1
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 3.2
Simplify the equation and keep it in point-slope form.
Step 4
Write in form.
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Step 4.1
Solve for .
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Step 4.1.1
Simplify .
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Step 4.1.1.1
Rewrite.
Step 4.1.1.2
Simplify by adding zeros.
Step 4.1.1.3
Apply the distributive property.
Step 4.1.1.4
Combine and .
Step 4.1.1.5
Cancel the common factor of .
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Step 4.1.1.5.1
Move the leading negative in into the numerator.
Step 4.1.1.5.2
Cancel the common factor.
Step 4.1.1.5.3
Rewrite the expression.
Step 4.1.2
Move all terms not containing to the right side of the equation.
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Step 4.1.2.1
Add to both sides of the equation.
Step 4.1.2.2
Add and .
Step 4.2
Reorder terms.
Step 4.3
Remove parentheses.
Step 5