Inequalities & Graphing
Slope of Parallel & Perpendicular Lines
Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals of each other (flip and negate).
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Worked Examples
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Problem
A line has slope 3. What is the slope of a parallel line?
Step-by-Step Solution
Parallel lines have the same slope.
The parallel line also has slope 3.
Answer
m = 3
Problem
A line has slope 2. What is the slope of a perpendicular line?
Step-by-Step Solution
Perpendicular slope = negative reciprocal.
Flip 2 to get 1/2, then negate: −1/2.
Answer
m = −1/2
Problem
Are lines with slopes 3/4 and −4/3 perpendicular?
Step-by-Step Solution
Check: multiply the slopes together.
(3/4) × (−4/3) = −12/12 = −1
Product = −1 → Yes, they are perpendicular!
Answer
Yes, perpendicular (product of slopes = −1)
Problem
A line has slope −3/5. What is the slope of a perpendicular line?
Step-by-Step Solution
Perpendicular slope = negative reciprocal.
Flip −3/5 to get −5/3, then negate: 5/3.
Answer
m = 5/3
Problem
Two lines have equations y = 2x + 1 and y = 2x − 7. Are they parallel, perpendicular, or neither?
Step-by-Step Solution
Both lines have slope m = 2.
Equal slopes → the lines are parallel.
Answer
Parallel (same slope, different y-intercepts)
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Slope of a line parallel to m = −5?
Slope of a line perpendicular to m = 4?
Slope of a line perpendicular to m = −2/3?
Are slopes 1/2 and −2 perpendicular?
Slope of a line parallel to m = 0?
Slope of a line perpendicular to m = 1?
Are slopes 3 and 3 parallel or perpendicular?
Slope of a line perpendicular to m = −5?
Are slopes 2/3 and −3/2 perpendicular?
Slope of a line parallel to y = 7x − 3?
Slope of a line perpendicular to y = −x + 2?
Two lines have slopes 4 and 1/4. Are they perpendicular?
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