Point Slope Form Calculator. Enter a point (x₁, y₁) and a slope (m) — or two points — and the Point Slope Form Calculator returns the line equation in point-slope form, slope-intercept form (y = mx + b), and standard form (Ax + By = C). Switch between Point + Slope and Two Points mode using the input selector. Also try the calculate Reverse FOIL Factored Form.
Point-slope form is a way to write the equation of a straight line when you know a point on the line and its slope. The formula is y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is the known point. It's the most direct way to express a line without first finding the y-intercept. See also our calculate Adding and Subtracting Polynomials.
The slope (m) measures how steep a line is — it's the ratio of the vertical change to the horizontal change between any two points on the line: m = (y₂ − y₁) / (x₂ − x₁). A positive slope means the line rises left to right, a negative slope means it falls, and a zero slope means the line is horizontal.
Plug the known values into the point-slope formula: y − y₁ = m(x − x₁). For example, with point (2, 3) and slope 8, you get y − 3 = 8(x − 2). You can leave it in this form or simplify to slope-intercept form y = 8x − 13.
Expand the right side of y − y₁ = m(x − x₁) and then isolate y. For example, y − 3 = 8(x − 2) becomes y − 3 = 8x − 16, and then y = 8x − 13. The result is in slope-intercept form y = mx + b, where b is the y-intercept.
After expanding point-slope form and collecting like terms, rearrange so that x and y are on the left side and the constant is on the right: Ax + By = C. Using the example above, y = 8x − 13 becomes −8x + y = −13, or equivalently 8x − y = 13. Multiply through to eliminate fractions if needed.
Yes — switch to Two Points mode and enter both coordinates (x₁, y₁) and (x₂, y₂). The calculator first computes the slope as m = (y₂ − y₁) / (x₂ − x₁), then applies the point-slope formula using the first point and the computed slope.
When the slope m = 0, the point-slope equation y − y₁ = 0·(x − x₁) simplifies to y = y₁. This represents a horizontal line passing through the given point at constant height y₁.
Yes — when the known point is the y-intercept (i.e., x₁ = 0), then y − y₁ = m(x − 0) simplifies directly to y = mx + y₁, which matches slope-intercept form y = mx + b. In all other cases, the two forms look different but represent the same line. You might also find our Radical Calculator useful.