Point Slope Form Calculator

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.

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.