What you’ll learn
Define parallel and perpendicular lines.
Key idea
For two nonvertical perpendicular lines, the slope product is negative one.
Perpendicular nonvertical slopes multiply to negative one; intercept and positive reciprocal do not determine perpendicularity.
Worked example
Enter the exact value or ordered values in the format requested below.
Line y=(-3)x+(-2). Find slope of a nonvertical line perpendicular to it.
- The supplied nonvertical line has slope -3.
- A perpendicular slope n satisfies (-3)n=-1, hence n=1/3; intercepts do not enter this product.
Answer: 1/3
Quick Check
Evaluate a worked attempt at define parallel and perpendicular lines, identify the first invalid step, and provide the correction.
Line y=(-4/7)x+(2). Student: Step 1, the reciprocal of its slope is -7/4. Step 2, this reciprocal is its perpendicular slope. Identify the first invalid step and correct the result.