Math
X and Y Intercepts Calculator
Set y = 0 to find where a graph crosses the x-axis and x = 0 to find where it crosses the y-axis. mathcheck does both for any line (slope-intercept, two points, point-slope, standard, or general form) and for quadratics, showing exact fractions or simplified radicals plus each substitution step.
Type a fraction like 3/2 or a decimal like -0.5. Type "undefined" for a vertical line.
Where the line crosses the y-axis.
Try an example
Result
X-intercept(s)
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- Y-intercept
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- Equation
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- Standard form / vertex
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- Slope / opening
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Study path
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What are x- and y-intercepts?
The y-A point where a graph crosses an axis. is the point where a graph crosses the y-axis; every point on that axis has x = 0, so substitute x = 0 and solve for y. The x-intercept is where the graph crosses the x-axis, where y = 0, so substitute y = 0 and solve for x. A line has at most one of each; a parabola can have zero, one, or two x-intercepts.
Intercepts by equation type
| Equation | x-intercept | y-intercept |
|---|---|---|
| y = mx + b | (-b/m, 0) | (0, b) |
| Ax + By = C | (C/A, 0) | (0, C/B) |
| y = k (horizontal) | none unless k = 0 | (0, k) |
| x = k (vertical) | (k, 0) | none unless k = 0 |
| y = ax^2 + bx + c | roots of the quadratic (0, 1, or 2 of them) | (0, c) |
How to use this calculator
- Pick Line or Quadratic.
- For a line, choose the form you have and enter it. How steep a line is: how much y changes for each step right in x. accept fractions like 3/2.
- For a quadratic, enter a, b, and c from y = ax^2 + bx + c.
- Read the intercepts as points. Exact fractions or A root expression written with the √ symbol, such as a square root. come first, decimals in parentheses.
- Open Show the work to see each substitution.
How to read the answer
Each intercept is written as an ordered pair so you can plot it directly: the x-intercept always has a 0 second coordinate and the y-intercept always has a 0 first coordinate. For a quadratic, two x-intercepts mean the parabola crosses the axis twice, one means it just touches at the The turning point of a parabola, or a corner point of a shape., and none means it stays entirely above or below the axis.
Common mistakes and edge cases
- Swapping the intercepts: the x-intercept comes from setting y = 0, not x = 0.
- Writing an intercept as a single number when the question asks for a point; (3, 0) and 3 are not the same answer.
- Expecting every line to have both intercepts. Horizontal lines (except y = 0) have no x-intercept and vertical lines (except x = 0) have no y-intercept.
- Forgetting the ± in the quadratic formula and reporting only one x-intercept.
- Treating a negative The b² − 4ac part of the quadratic formula; its sign tells you how many real solutions exist. as an error; it simply means there are no real x-intercepts.
Worked examples
Line in slope-intercept form
y = (3/2)x + 1
X-intercept(s)
(-2/3, 0) ≈ (-0.6667, 0)
Line in standard form
2x + 3y = 12
X-intercept(s)
(6, 0)
Line from two points
Through (-2, 7) and (4, -5)
X-intercept(s)
(3/2, 0) ≈ (1.5, 0)
Horizontal line
y = 4
X-intercept(s)
none (horizontal line never reaches the x-axis)
Quadratic with two x-intercepts
y = x^2 - 4x + 3
X-intercept(s)
(1, 0) and (3, 0)
Quadratic with irrational roots
y = x^2 + 2x - 1
X-intercept(s)
(-1 - √2 (-2.4142), 0) and (-1 + √2 (0.4142), 0)
Quadratic with no x-intercepts
y = x^2 + 1
X-intercept(s)
none (the parabola never crosses the x-axis)
Not a quadratic
a = 0
X-intercept(s)
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Frequently asked questions
How do I find the x-intercept of a line?+
Substitute y = 0 and solve for x. For y = 2x - 6, 0 = 2x - 6 gives x = 3, so the x-intercept is (3, 0).
How do I find the y-intercept?+
Substitute x = 0 and solve for y. In y = mx + b the y-intercept is simply b, and in Ax + By = C it is C/B.
Can a line have no x-intercept?+
Yes. A horizontal line y = k with k ≠ 0 runs parallel to the x-axis and never crosses it. Similarly a vertical line x = k with k ≠ 0 has no y-intercept.
How many x-intercepts can a parabola have?+
Zero, one, or two, depending on the discriminant b^2 - 4ac: negative means none, zero means one (the vertex touches the axis), positive means two.
Are x-intercepts the same as roots or zeros?+
Yes. The x-intercepts of y = f(x) are the values of x where f(x) = 0, also called the roots or zeros of the function.
What is intercept form of a line?+
x/a + y/b = 1, where a is the x-intercept and b is the y-intercept. It only works when both intercepts exist and are nonzero.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026