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The slope of a line passing through (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1). The slope-intercept form is y = mx + c. Parallel lines share equal slopes (m1 = m2). Perpendicular lines have negative reciprocal slopes (m1 × m2 = -1).
Distance formula: d = √((x2 - x1)2 + (y2 - y1)2). Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2).
Worked example
1.Two non-vertical lines are perpendicular if and only if the product of their slopes equals -1.
2.The distance between (0, 0) and (3, 4) is 7.
3.The midpoint between (-2, 4) and (6, 8) is (2, 6).
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