Education
Point Slope Form Calculator
Pick slope-plus-point or two-points input. The calculator returns the point-slope equation y − y₁ = m(x − x₁) along with the slope-intercept form and the slope itself.
From
Point-slope form sits between "slope" and "slope-intercept": it captures both the slope and a specific point in one equation. Solve for y to convert to slope-intercept form.
Point-slope form
y − 4 = 2(x − 3)
Slope m = 2; through (3, 4)
Use point-slope form when you know the slope and a specific point but not the y-intercept. Distribute m and add y₁ to both sides to convert to slope-intercept form.
Examples
Slope 2, point (3,4)
y − 4 = 2(x − 3); y = 2x − 2
Two points (1,2), (4,11)
m = 3; y − 2 = 3(x − 1); y = 3x − 1
Slope −0.5, point (0,5)
y − 5 = −0.5(x); y = −0.5x + 5
Horizontal: slope 0, point (2,7)
y − 7 = 0; y = 7
How it works
Point-slope form is the equation built directly from the slope and a known point. It comes from rearranging the slope formula: if (x, y) is any point on the line and (x₁, y₁) is a known point, then (y − y₁) / (x − x₁) = m.
Point-slope · y − y₁ = m(x − x₁)
Two-point slope · m = (y₂ − y₁) / (x₂ − x₁)
Related calculators
- Slope calculator when you only need the slope between two points.
- Slope intercept form calculator when you want y = mx + b as the primary output.
- Distance formula calculator for the distance between two points.
- Midpoint formula calculator for the midpoint between two points (useful for perpendicular bisectors).
- All education calculators.
Frequently asked questions
y − y₁ = m(x − x₁). It is a way to write the equation of a line using its slope m and any one point (x₁, y₁) on the line. The form makes it easy to plug in a point you already know.
Point-slope is best when you know a specific point and the slope but not the y-intercept (b in y = mx + b). It is also the natural form to write when a problem hands you a point and a slope directly.
Distribute m on the right side, then add y₁ to both sides. The calculator does this and shows the slope-intercept equivalent next to the point-slope form.
First compute the slope m = (y₂ − y₁) / (x₂ − x₁). Then pick either point and substitute into y − y₁ = m(x − x₁). The calculator handles both steps.
A vertical line has undefined slope. Point-slope form y − y₁ = m(x − x₁) needs a finite m, so vertical lines can only be written as x = constant. The calculator detects this case and flags it.
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