The y-intercept is the value of y when x = 0 – the starting value of a linear model, such as a fixed fee before any usage is charged.
How to use the y Intercept Calculator
- My line is given as
- a
- b
- c
- Slope m
- Intercept c
- x₁
- y₁
- x₂
- y₂
Results update as you type, and everything is calculated in your browser.
How it works
Choose how your line is given. The y-intercept is found by setting x = 0 in its equation.
Inputs explained
| Field | What to enter |
|---|---|
| My line is given as | Choose one: ax + by + c = 0, y = mx + c, Two points |
| a | A number |
| b | A number |
| c | A number |
| Slope m | A number |
| Intercept c | A number |
| x₁ | A number |
| y₁ | A number |
| x₂ | A number |
| y₂ | A number |
Example values
How the main result changes when a changes and everything else stays at the example values above:
| a | y-intercept |
|---|---|
| 1 | 2 |
| 1.5 | 2 |
| 2 | 2 |
| 2.5 | 2 |
| 3 | 2 |
| 4 | 2 |
Formula
General: y-intercept = −c/b, x-intercept = −c/a, slope = −a/b
Two points: m = (y₂ − y₁)/(x₂ − x₁), y-intercept = y₁ − m·x₁
Worked example
Inputs — My line is given as: ax + by + c = 0; a: 2; b: -4; c: 8.
Results — y-intercept = 2; x-intercept = -4; Slope = 0.5.
Key terms
- Intercept
- A point where a graph crosses an axis.
Frequently asked questions
What is the y-intercept of 2x − 4y + 8 = 0?
2 (set x = 0: −4y + 8 = 0).
Can a line have no y-intercept?
A vertical line other than x = 0 never crosses the y-axis.
What is the x-intercept?
Where the line crosses the x-axis (y = 0).
How do I find the intercept of y = 3x − 5?
It is −5, the constant term.