College Algebra / Unit 3 Alg 148 worked example, 60 to 90 seconds
Writing a Line from Two Points
The idea
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.
In practice
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.
Where people slip
Compute the slope before reaching for point-slope; the formula's m is not optional.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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