Point-Slope Form Calculator
Enter a point and a slope to get the line in point-slope form (and every other form).
Last updated: June 22, 2026 · Reviewed by TG we-Calculate Editorial TeamPoint (x₁, y₁)
- 1
Slope × x₁
2 × 2 = 4 - 2
Y-intercept b
3 − 4 = -1Rearranging y = mx + b isolates the y-intercept: b = y₁ − m × x₁.
Formula
How this is calculated
Point-slope form expresses a line directly from one point on it and its slope. If a line has slope m and passes through (x₁, y₁), then for every other point (x, y) on the line the slope between them must also equal m: (y − y₁) ÷ (x − x₁) = m. Multiplying both sides by (x − x₁) gives the point-slope equation y − y₁ = m(x − x₁).
This form is the quickest to write because it needs no algebra — you just substitute the point and slope. To get slope-intercept form, expand and solve for y, which gives y = mx + b with b = y₁ − m·x₁. Standard form (Ax + By = C) follows by moving the x-term across and clearing any fractions.
A slope of 0 gives a horizontal line y = y₁; the point-slope and slope-intercept forms then both collapse to y = y₁.
Examples
| Input | Result |
|---|---|
| point (2, 3), slope 2 | y − 3 = 2(x − 2) → y = 2x − 1 |
Frequently asked questions
y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is a point on the line.
Distribute the slope and add y₁ to both sides to isolate y: y = mx + (y₁ − m·x₁).
Also known as
Sources & references
TG we-Calculate Editorial Team. (2026). Point-Slope Form Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/point-slope-form-calculator
TG we-Calculate Editorial Team. "Point-Slope Form Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/point-slope-form-calculator.
TG we-Calculate Editorial Team, "Point-Slope Form Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/point-slope-form-calculator
@misc{wecalculate_point_slope_form_calculator, title = {Point-Slope Form Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/point-slope-form-calculator}}, year = {2026}, note = {TG we-Calculate} }
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