Use coordinates to prove simple geometric theorems, including simple circle theorems.
Interpret a coordinate-proof result as a geometric conclusion
Problem
What does this coordinate-proof result mean geometrically: \(\text{two}~\text{distinct}~\text{nonvertical}~\text{lines}\) have equal slopes?
Big Picture
What this problem is really about
Numerical slope evidence has to be translated according to what slope actually measures: direction. We’ll interpret equality as the same direction, use the stated distinctness to rule out coincidence, identify the resulting relationship between the full lines, and avoid drawing any unsupported conclusion about finite segment lengths.
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