What you’ll learn
Use slope criterion for parallel lines.
Key idea
Distinct nonvertical parallel lines have equal signed slopes.
Equal finite slopes establish parallel direction, while the offset guarantees distinct lines.
Worked example
Enter the exact value or ordered values in the format requested below.
Line l passes through A=(-3, -2), B=(-1, 3). A distinct line n through Q=(-3, -1) must be parallel to l. Find the slope of n.
- Line l has slope 5/2=5/2.
- Parallel n keeps slope 5/2; Q is one unit vertically from A at the same x, hence n is distinct.
Answer: 5/2
Quick Check
Evaluate a worked attempt at use slope criterion for parallel lines, identify the first invalid step, and provide the correction.
Line l through A=(-3, 0), B=(-2, -5) has slope -5. Student Step 1 connects parallelism to slope. Step 2 gives a parallel line through Q=(-3, 1) slope 1/5 by negative reciprocation. Locate and repair the first invalid step.