Type any equation in x and y, or a function y = f(x), and get every x-intercept and y-intercept as exact values with the working shown. For straight lines you also get the slope and the slope-intercept, standard and intercept forms, and every result is marked on an interactive graph.
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Examples:
Type any equation such as 4x − y = 8, y = x² − 9 or x²/4 + y²/9 = 1. Without an equals sign the input is read as y = f(x). Supported: + − * / ^, implicit multiplication (2x, 3(x+1)), sqrt, cbrt, abs or |x|, ln, log, exp, sin, cos, tan, pi, e.
Enter two points on a straight line. The calculator finds the slope, the equation of the line and both intercepts.
x-intercepts
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y-intercepts
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Step-by-step
Graph
x-intercept y-intercept
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How to use the X and Y Intercept Calculator
Type the equation, such as 2x + 3y = 6, y = x^2 - 4x + 3 or x^2 + y^2 = 25, or tap one of the examples. A plain expression like x^2 - 9 is read as y = x² − 9.
Or switch to Two points and enter the coordinates of two points on a line.
Press Find intercepts (or Enter).
Read the intercepts in the two result cards, written as points (a, 0) and (0, b).
Follow the steps to see how each intercept is found, and check the graph, where x-intercepts are orange and y-intercepts green.
What intercepts are and how to find them
An intercept is a point where a graph meets an axis. Every point on the x-axis has y = 0, and every point on the y-axis has x = 0, so the rule is the same for any equation:
x-intercepts: put y = 0 into the equation and solve for x. Each answer a is the point (a, 0). These are also called the zeros or roots of a function.
y-intercepts: put x = 0 into the equation and solve for y. Each answer b is the point (0, b). For a function this is just f(0).
The point (0, 0) is both an x- and a y-intercept when the graph passes through the origin.
Intercept shortcuts for common equations
Equation
x-intercept(s)
y-intercept
Example
Slope-intercept y = mx + b (m ≠ 0)
(−b/m, 0)
(0, b)
y = 2x − 6 → (3, 0) and (0, −6)
Standard form Ax + By = C
(C/A, 0)
(0, C/B)
4x + 5y = 20 → (5, 0) and (0, 4)
Intercept form x/a + y/b = 1
(a, 0)
(0, b)
x/3 + y/2 = 1 → (3, 0) and (0, 2)
Horizontal line y = k
none (unless k = 0)
(0, k)
y = 4 → only (0, 4)
Vertical line x = h
(h, 0)
none (unless h = 0)
x = −2 → only (−2, 0)
Quadratic y = ax² + bx + c
(−b ± √(b² − 4ac))/(2a), if b² − 4ac ≥ 0
(0, c)
y = x² − 4x + 3 → (1, 0), (3, 0) and (0, 3)
Factored y = a(x − r)(x − s)
(r, 0) and (s, 0)
(0, a·r·s)
y = 2(x − 1)(x + 4) → (1, 0), (−4, 0), (0, −8)
Circle x² + y² = r²
(−r, 0) and (r, 0)
(0, −r) and (0, r)
x² + y² = 25 → (±5, 0) and (0, ±5)
Rational y = (x − p)/(x − q)
(p, 0), if p ≠ q
(0, p/q), if q ≠ 0
y = (x − 2)/(x + 1) → (2, 0) and (0, −2)
Exponential y = a·bˣ + k
one if −k/a > 0, else none
(0, a + k)
y = 2ˣ − 8 → (3, 0) and (0, −7)
Tips for checking your answers
Plug the point back in. An x-intercept (a, 0) must satisfy the original equation with x = a and y = 0. If it does not, an arithmetic step went wrong.
Use intercepts to sketch a line quickly. Two intercepts are two points, so marking them and joining them with a ruler draws the whole line. This fails only for lines through the origin, where both intercepts are the same point and you need one more point.
Watch the domain. A function like y = √(x + 4) − 1 or y = ln(x) may not be defined at x = 0, and then it has no y-intercept at all.
Repeated roots touch the axis. In y = (x − 2)², the root x = 2 appears twice, so the parabola touches the x-axis at (2, 0) and turns back without crossing it.
Frequently asked questions
How do you find the x-intercept?
Set y = 0 in the equation and solve for x. Each solution a gives an x-intercept at the point (a, 0). For 2x + 3y = 6, setting y = 0 gives 2x = 6, so the x-intercept is (3, 0).
How do you find the y-intercept?
Set x = 0 and solve for y. Each solution b gives a y-intercept at (0, b). For 2x + 3y = 6, setting x = 0 gives 3y = 6, so the y-intercept is (0, 2). In y = mx + b form the y-intercept is simply b.
Can a function have more than one y-intercept?
No. A function gives exactly one y-value for each x, so it can cross the y-axis at most once (and not at all if x = 0 is outside its domain). Curves that are not functions, such as the circle x² + y² = 25, can have two y-intercepts: (0, −5) and (0, 5).
How many x-intercepts can a quadratic have?
Zero, one or two, decided by the discriminant b² − 4ac. If it is positive the parabola crosses the x-axis twice, if it is zero it touches the axis once at its vertex, and if it is negative it never reaches the x-axis.
What are the intercepts of a horizontal or vertical line?
A horizontal line y = k has the y-intercept (0, k) and no x-intercept unless k = 0, in which case it is the x-axis itself. A vertical line x = h has the x-intercept (h, 0) and no y-intercept unless h = 0.
What is the intercept form of a line?
A line that crosses the axes at (a, 0) and (0, b), with a and b not zero, can be written as x/a + y/b = 1. For example, 2x + 3y = 6 divided by 6 becomes x/3 + y/2 = 1, so the intercepts are 3 and 2.
Why does the calculator say an answer is approximate?
Equations such as 2^x = x + 3 or cos(x) = x have no simple exact solution, so the roots are found numerically and shown with six decimal places. Whenever a root is a whole number, a fraction, a simple radical from a quadratic or a multiple of π, the exact value is shown instead.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.