Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Use slope to prove distinct lines are parallel
Problem
Calculate the slopes of the lines through \((0,1)\) and \((2,5)\), and through \((3,-1)\) and \((5,3)\). Use the results to establish that the lines are parallel.
Use slope as a direction test: calculate rise over run for each point pair with the subtraction order kept consistent. Matching slopes establish the same direction, but they prove parallel lines only after you also confirm the lines are distinct, for example by showing that they have different intercepts.
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