Lines have many equation forms — pick the one that matches what you know.
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y = m·x + b
Got a point and a slope? Use point-slope: y − y₁ = m(x − x₁), then expand to y = mx + b if you want slope-intercept form.
Your turn
Find the slope-intercept equation of the line through (2, 1) and (4, 7).
Recap
- Slope-intercept y = mx + b: easiest to graph.
- Point-slope y − y₁ = m(x − x₁): best when you know a point and the slope.
- All forms describe the same line — convert freely.
Three common forms
- Slope-intercept: y = mx + b — m is slope, b is y-intercept.
- Point-slope: y − y₁ = m(x − x₁) — slope and one point.
- Two-point: m = (y₂ − y₁)/(x₂ − x₁) — derive slope first.
Try it
Line through (1, 2) with slope 3
y − 2 = 3(x − 1) → y = 3x − 1.