Point-Slope Form Calculator
Enter a point and slope to instantly see the line equation in point-slope form, slope-intercept form, and standard form. This calculator also finds the x-intercept and y-intercept.
Point-slope form is one of three standard ways to write the equation of a line. It is especially useful when you know a point on the line and the slope.
Point-Slope Form:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a known point and m is the slope.
Converting to Slope-Intercept Form (y = mx + b):
Distribute and solve for y: y - y₁ = m(x - x₁) y = mx - mx₁ + y₁ y = mx + b, where b = y₁ - mx₁
For point (3, 7) with slope 2: y - 7 = 2(x - 3), which becomes y = 2x - 6 + 7 = 2x + 1.
Converting to Standard Form (Ax + By = C):
Rearrange y = mx + b so that x and y terms are on one side. Multiply through to clear fractions if needed, and make A positive by convention.
From y = 2x + 1: -2x + y = 1, or 2x - y = -1.
When to use each form:
- Point-slope: when you know a point and the slope.
- Slope-intercept: when you need to graph quickly or identify the y-intercept.
- Standard: when working with systems of equations or integer coefficients.