# What is the y intercept of my line?

Finds the y-intercept b of a line, where it crosses the y axis, and its x-intercept, from two points, a slope and a point, or Ax + By = C, in exact fractions with a graph.

- Page: https://www.acalculator.org/math/slope-intercept-form-calculator
- JSON spec: https://www.acalculator.org/math/slope-intercept-form-calculator.json
- Version: 4bddcd50a02c

## Default answer

Example with the default inputs (I know Two points, x₁ 2, y₁ -1, x₂ -5, y₂ 3): The line y = −(4/7)x + 1/7 crosses the y axis at (0, 1/7).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| given | I know | What you know about the line: two points on it, its slope and one point, or its standard form. |
| x1 | x₁ | The x coordinate of a point on the line. |
| y1 | y₁ | The y coordinate of the same point. |
| x2 | x₂ | The x coordinate of a second point on the line. |
| y2 | y₂ | The y coordinate of the second point. |
| m | Slope (m) | How much y changes when x goes up by 1. |
| a | A | The number in front of x in Ax + By = C. |
| b | B | The number in front of y in Ax + By = C. |
| c | C | The number on the right of Ax + By = C. |
| x | x | Optional: an x value at which to read y on the line. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| intercept | y-intercept b | Where the line crosses the y axis: the value of y at x = 0. |
| yPoint | y-intercept point | The point (0, b) where the line crosses the y axis, as exact fractions. |
| xIntercept | x-intercept | Where the line crosses the x axis: the value of x at y = 0, −b ÷ m. None for a flat line. |
| xPoint | x-intercept point | The point (−b ÷ m, 0) where the line crosses the x axis, as exact fractions. None for a flat line, except y = 0, which is the x axis. |
| equation | Slope-intercept form | The line as y = mx + b, with the slope m and the y-intercept b as exact fractions. |
| slope | Slope m | The rise over the run: (y₂ − y₁) ÷ (x₂ − x₁). |
| standard | Standard form | The same line as Ax + By = C, with whole numbers A, B, C that share no factor. |
| y | y on the line | The y value on the line at the x you typed: mx + b. |

## Method

m = (y₂ − y₁) ÷ (x₂ − x₁) (or the slope as typed), b = y₁ − m × x₁; from Ax + By = C, m = −A ÷ B and b = C ÷ B. The y-intercept is (0, b) and the x-intercept is (−b ÷ m, 0); all in exact fractions.

## Assumptions

- Every number is read exactly as typed: 0.1 is 1/10, so the intercepts are exact fractions.
- A vertical line (two points with the same x, or B = 0) has no y-intercept here; a flat line (m = 0) has no x-intercept, except y = 0, which is the x axis.
- y at x is shown when it is at most 10³⁰⁰ in size.

## Worked examples

1. given = points, x1 = 2, y1 = -1, x2 = -5, y2 = 3 gives intercept = 0.142857, yPoint = (0, 1/7), slope = -0.571429, xIntercept = 0.25, xPoint = (1/4, 0), equation = y = −(4/7)x + 1/7, standard = 4x + 7y = 1. Source: OpenStax, Algebra and Trigonometry 2e, §2.2 Linear Equations in One Variable (slope formula, y = mx + b, standard form Ax + By = C; Example 10: slope −3 through (4, 8) gives y = −3x + 20; Example 12: slope −6 through (1/4, −2) gives 12x + 2y = −1), https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-2-linear-equations-in-one-variable (retrieved 2026-10-02).
2. given = slope, m = -3, x1 = 4, y1 = 8, x = 1 gives intercept = 20, equation = y = −3x + 20, xIntercept = 6.666667, xPoint = (20/3, 0), y = 17. Source: OpenStax, Algebra and Trigonometry 2e, §2.2 Linear Equations in One Variable (slope formula, y = mx + b, standard form Ax + By = C; Example 10: slope −3 through (4, 8) gives y = −3x + 20; Example 12: slope −6 through (1/4, −2) gives 12x + 2y = −1), https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-2-linear-equations-in-one-variable (retrieved 2026-10-02).
3. given = standard, a = 12, b = 2, c = -1 gives intercept = -0.5, yPoint = (0, −1/2), slope = -6, xIntercept = -0.083333, xPoint = (−1/12, 0). Source: OpenStax, Algebra and Trigonometry 2e, §2.2 Linear Equations in One Variable (slope formula, y = mx + b, standard form Ax + By = C; Example 10: slope −3 through (4, 8) gives y = −3x + 20; Example 12: slope −6 through (1/4, −2) gives 12x + 2y = −1), https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-2-linear-equations-in-one-variable (retrieved 2026-10-02).
4. given = slope, m = -3, x1 = 0, y1 = -4 gives intercept = -4, yPoint = (0, −4), xIntercept = -1.333333, xPoint = (−4/3, 0). Source: OpenStax, Algebra and Trigonometry 2e, §2.1 The Rectangular Coordinate Systems and Graphs (set x = 0 for the y-intercept and y = 0 for the x-intercept; y = −3x − 4 crosses at (0, −4) and (−4/3, 0)), https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-1-the-rectangular-coordinate-systems-and-graphs (retrieved 2026-10-02).
5. given = points, x1 = -2, y1 = 5, x2 = 4, y2 = 5 gives intercept = 5, slope = 0, equation = y = 5. Source: OpenStax, Algebra and Trigonometry 2e, §2.1 The Rectangular Coordinate Systems and Graphs (set x = 0 for the y-intercept and y = 0 for the x-intercept; y = −3x − 4 crosses at (0, −4) and (−4/3, 0)), https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-1-the-rectangular-coordinate-systems-and-graphs (retrieved 2026-10-02).

## FAQ

### What is the y-intercept?

The point where a line crosses the y axis. There x = 0, so the point is (0, b), and b is the number added at the end of y = mx + b. For y = −3x + 20 the y-intercept is (0, 20).

### How do I find the y-intercept from two points?

Find the slope first, m = (y₂ − y₁) ÷ (x₂ − x₁). Then put one point into y = mx + b and solve for b: b = y₁ − m × x₁. For (2, −1) and (−5, 3): m = 4 ÷ (−7) = −4/7 and b = −1 − (−4/7) × 2 = 1/7.

### How do I find the y-intercept from Ax + By = C?

Set x = 0: then By = C, so b = C ÷ B. For 12x + 2y = −1, b = −1 ÷ 2 = −1/2. The x-intercept comes from setting y = 0: x = C ÷ A = −1/12.

### How do I find the x-intercept?

Set y = 0 and solve 0 = mx + b, which gives x = −b ÷ m. For y = −3x − 4 that is x = −4/3, so the line crosses the x axis at (−4/3, 0).

### Can a line have no y-intercept?

Yes, a vertical line x = c with c not 0. It never meets the y axis (the y axis itself, x = 0, meets it everywhere). Two points with the same x, or B = 0 in Ax + By = C, give a vertical line, and the calculator says so.

### Can a line have no x-intercept?

Yes, a flat line y = b with b not 0, such as y = 5. Its slope is 0, so −b ÷ m has no value. The calculator leaves the x-intercept out.

### Why are the answers fractions?

Each number you type is read exactly (0.1 is 1/10), so the slope and intercepts are exact fractions such as 1/7. The decimal value of the y-intercept is shown as the headline too.

## Sources

- OpenStax, Algebra and Trigonometry 2e, §2.2 Linear Equations in One Variable (slope formula, y = mx + b, standard form Ax + By = C; Example 10: slope −3 through (4, 8) gives y = −3x + 20; Example 12: slope −6 through (1/4, −2) gives 12x + 2y = −1). https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-2-linear-equations-in-one-variable (retrieved 2026-10-02)
- OpenStax, Algebra and Trigonometry 2e, §2.1 The Rectangular Coordinate Systems and Graphs (set x = 0 for the y-intercept and y = 0 for the x-intercept; y = −3x − 4 crosses the axes at (0, −4) and (−4/3, 0)). https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-1-the-rectangular-coordinate-systems-and-graphs (retrieved 2026-10-02)