What is the y intercept of my line?
Type two points on a line, its slope and one point, or its standard form Ax + By = C. The y intercept calculator gives b, the point where the line crosses the y axis, the x-intercept, and the line as y = mx + b, in exact fractions with a graph.
- y-intercept b
- 0.142857
The line y = −(4/7)x + 1/7 crosses the y axis at (0, 1/7).
- y-intercept point
- (0, 1/7)
- x-intercept
- 0.25
- x-intercept point
- (1/4, 0)
- Slope-intercept form
- y = −(4/7)x + 1/7
- Slope m
- -0.571429
- Standard form
- 4x + 7y = 1
y-intercept b: 0.142857. The line y = −(4/7)x + 1/7 crosses the y axis at (0, 1/7).
y on the line by x
How to calculate
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.
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).
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.
- 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
Each example is checked against the calculator on every build.
- I know Two points, x₁ 2, y₁ -1, x₂ -5, y₂ 3 gives y-intercept b 0.142857, y-intercept point (0, 1/7), Slope m -0.571429, x-intercept 0.25, x-intercept point (1/4, 0), Slope-intercept form y = −(4/7)x + 1/7, Standard form 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)
- I know Slope and a point, Slope (m) -3, x₁ 4, y₁ 8, x 1 gives y-intercept b 20, Slope-intercept form y = −3x + 20, x-intercept 6.666667, x-intercept point (20/3, 0), y on the line 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)
- I know Ax + By = C, A 12, B 2, C -1 gives y-intercept b -0.5, y-intercept point (0, −1/2), Slope m -6, x-intercept -0.083333, x-intercept point (−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)
- I know Slope and a point, Slope (m) -3, x₁ 0, y₁ -4 gives y-intercept b -4, y-intercept point (0, −4), x-intercept -1.333333, x-intercept point (−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)
- I know Two points, x₁ -2, y₁ 5, x₂ 4, y₂ 5 gives y-intercept b 5, Slope m 0, Slope-intercept form 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)
How it works
A line that is not vertical is y = mx + b. Its y-intercept is the point (0, b), where x = 0. Its x-intercept is the point where y = 0: x = −b ÷ m.
From two points (x₁, y₁) and (x₂, y₂): m = (y₂ − y₁) ÷ (x₂ − x₁), then b = y₁ − m × x₁.
From a slope m and a point (x₁, y₁): b = y₁ − m × x₁.
From Ax + By = C: solve for y, so y = (−A ÷ B)x + C ÷ B. The slope is m = −A ÷ B and b = C ÷ B.
The calculator also shows the line as y = mx + b, the standard form Ax + By = C (whole numbers with no common factor, A ≥ 0, and B > 0 when A = 0), the slope, and y at an x you choose (y = mx + b). The graph draws y for x from −10 to 10.
Rules
- Every number is read exactly as typed, as a fraction: 0.1 is 1/10. The slope and intercepts are exact fractions in lowest terms.
- Two points with the same x lie on a vertical line, which has no slope and no y-intercept: no answer. Two equal points do not set a line: no answer.
- In Ax + By = C, B = 0 is a vertical line (no answer), and A = B = 0 is not a line (no answer).
- A flat line (m = 0) has no x-intercept; it is left out. The one exception is y = 0, the x axis itself: its x-intercept point reads “every point (the line is the x axis)” and the x-intercept number is left out.
- A y-intercept beyond the largest double-precision number has no answer. Other decimals beyond that range are left out; y at x is left out above 10³⁰⁰ in size.
Output format. Points as (x, y) with exact fractions such as 1/7 and a true minus sign (−1/2); the decimals are the exact fractions rounded to double precision. Equations are written as on the slope-intercept form page: 2x, (7/3)x, x, −x; a zero term is left out.
Worked examples by hand
Through (2, −1) and (−5, 3). m = (3 − (−1)) ÷ (−5 − 2) = 4 ÷ (−7) = −4/7. b = −1 − (−4/7) × 2 = −1 + 8/7 = 1/7, so the y-intercept is (0, 1/7), about 0.142857. The x-intercept is −(1/7) ÷ (−4/7) = 1/4. The line is y = −(4/7)x + 1/7, or 4x + 7y = 1.
Slope −3 through (4, 8). b = 8 − (−3) × 4 = 20, so y = −3x + 20. The x-intercept is −20 ÷ (−3) = 20/3. At x = 1, y = −3 + 20 = 17.
12x + 2y = −1. b = C ÷ B = −1/2; m = −12 ÷ 2 = −6. The x-intercept is C ÷ A = −1/12.
y = −3x − 4 (slope −3 through (0, −4)). The y-intercept is (0, −4) and the x-intercept is 4 ÷ (−3) = −4/3.
Through (−2, 5) and (4, 5). m = 0, so the line is y = 5: it crosses the y axis at 5 and never meets the x axis.
Other questions people ask
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.