BYTETOOLS

Slope Intercept Form Calculator

Find the equation of a line from two points or from a slope and a point. Get y = mx + b, point-slope and standard form, plus a drawn line graph.

2
Slope m
0
y-intercept b

Line equations

  • Slope-intercept: y = 2x + 0
  • Point-slope: y − 2 = 2(x − 1)
  • Standard form: 2x − y = 0

m = (y₂ − y₁) / (x₂ − x₁) = (6 − 2) / (3 − 1) = 4 / 2 = 2

Sketch

What is the Slope Intercept Form Calculator?

The ByteTools Slope Intercept Form Calculator finds the equation of a straight line. Give it two points, or one point plus a slope, and it returns the equation in slope-intercept form y = mx + b, in point-slope form y − y₁ = m(x − x₁), and in standard form Ax + By = C — with the slope and y-intercept calculation written out.

  • Two-point and slope-plus-point input modes
  • Slope-intercept, point-slope and standard (Ax + By = C) forms
  • Shows the rise-over-run slope calculation
  • Handles vertical (undefined slope) and horizontal lines correctly
  • Canvas line sketch with self-drawn axes and marked points
  • 100% private — runs entirely in your browser

How to use the Slope Intercept Form Calculator

  1. 1

    Choose input mode: two points, or slope and one point.

  2. 2

    Enter the coordinates (and the slope, if applicable).

  3. 3

    Read the equation in slope-intercept, point-slope and standard forms.

  4. 4

    Check the slope calculation and the line sketch with your points marked.

  5. 5

    Copy the equations or download the sketch as a PNG.

About the Slope Intercept Form Calculator

The ByteTools Slope Intercept Form Calculator finds the equation of a straight line. Give it two points, or one point plus a slope, and it returns the equation in slope-intercept form y = mx + b, in point-slope form y − y₁ = m(x − x₁), and in standard form Ax + By = C — with the slope and y-intercept calculation written out.

A small canvas sketch draws the line with axes, gridlines and your points marked, so you can see the slope's direction at a glance. Vertical lines are handled honestly: when both points share the same x, the tool reports undefined slope and gives the equation x = c instead of a bogus y = mx + b.

Everything runs 100% locally in your browser — no uploads, no accounts. It is designed for algebra and geometry students, tutors making examples, and anyone converting between line forms.

Frequently asked questions

How do you find slope-intercept form from two points?

First compute the slope m = (y₂ − y₁) / (x₂ − x₁), then substitute one point into y = mx + b to solve for b. For the points (1, 2) and (3, 6): m = 4/2 = 2, then b = 2 − 2(1) = 0, giving y = 2x. The calculator shows both steps.

What do m and b mean in y = mx + b?

m is the slope — how much y changes for each unit increase in x — and b is the y-intercept, the value of y where the line crosses the y-axis (at x = 0). A positive m slopes upward left to right; a negative m slopes downward.

What is the slope of a vertical line?

It is undefined, because the run x₂ − x₁ is zero and division by zero is impossible. A vertical line cannot be written as y = mx + b; its equation is simply x = c. This calculator detects that case and reports x = c rather than an error.

What is standard form of a line?

Standard form writes the line as Ax + By = C with A, B and C usually chosen as integers with no common factor and A ≥ 0. For example y = 2x + 1 becomes 2x − y = −1. The calculator converts automatically and clears fractions when the inputs allow it.

How is point-slope form different?

Point-slope form, y − y₁ = m(x − x₁), states the line using the slope and any single known point, without solving for the intercept. It is the natural first step when you know a point and a slope, and expanding it gives slope-intercept form. The tool shows both.

Related tools