Examples

Determine if Perpendicular
,
Step 1
Find the slope and y-intercept of the first equation.
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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
Reorder terms.
Step 1.2
Find the values of and using the form .
Step 2
Find the slope and y-intercept of the second equation.
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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
Simplify the right side.
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Step 2.1.2.1
Simplify each term.
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Step 2.1.2.1.1
Combine and .
Step 2.1.2.1.2
Move to the left of .
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
Find the values of and using the form .
Step 3
Compare the slopes of the two equations.
Step 4
Compare the decimal form of one slope with the negative reciprocal of the other slope. If they are equal, then the lines are perpendicular. If the they are not equal, then the lines are not perpendicular.
Step 5
The equations are perpendicular because the slopes of the two lines are negative reciprocals.
Perpendicular
Step 6
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