Slope-intercept form shows the two most useful facts about a line at a glance: its steepness m and where it crosses the y-axis, b. It is the form used for graphing and for linear models such as cost = fixed fee + rate × quantity.
How to use the Slope Intercept Form Calculator
- x₁
- y₁
- x₂
- y₂
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The slope comes from the two points and the intercept from substituting one point. Fractions are kept exact where possible.
Formula
m = (y₂ − y₁)/(x₂ − x₁), b = y₁ − m·x₁
Worked example
Inputs — x₁: 1; y₁: 2; x₂: 4; y₂: 3.
Results — y = mx + b = y = (1/3)x + 5/3; Slope m = 1/3 ≈ 0.33333333; y-intercept b = 5/3; Standard form = x − 3y = −5; Point-slope form = y − 2 = (1/3)(x − 1).
Key terms
- y-intercept
- Where a line crosses the y-axis.
Frequently asked questions
How do I find slope-intercept form from two points?
Compute m, then b = y₁ − m·x₁.
What is the x-intercept?
−b/m, where y = 0.
How do I graph y = mx + b?
Plot (0, b) and move 1 right and m up.
Can every line be written this way?
All except vertical lines.