Writing a Line from Two Points

Writing a line's equation from two points means computing the slope with the slope formula, then feeding the slope and either point to the point-slope formula.

Find the line through (1, 2) and (3, 8). Slope first: m = (8 − 2)/(3 − 1) = 6/2 = 3. Point-slope with (1, 2): y − 2 = 3(x − 1), which unwraps to y = 3x − 1. The other point runs the check: at x = 3, y = 3(3) − 1 = 8 — the line passes through (3, 8) as required. Either point works in the formula; the line that results is the same, because both points sit on it. The unused point is never wasted: it is the check.