Find the y-intercept of a line using your preferred input method. Enter a linear equation in slope-intercept or standard form, or provide two known points — the calculator returns the y-intercept value, the slope, and the full equation of the line so you can verify your work at a glance. Also try the Factoring Calculator.
Y-Intercept (b)
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Slope (m)
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Line Equation
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Y-Intercept Point
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The y-intercept is the point where a line crosses the y-axis, meaning where x = 0. It is commonly written as the coordinate (0, b), where b is the y-intercept value. In the slope-intercept form y = mx + b, the constant b directly represents the y-intercept. See also our Interval Notation — Inequality to Interval Notation.
To find the y-intercept from any linear equation, substitute x = 0 and solve for y. For example, in the equation 3x + 2y = 12, setting x = 0 gives 2y = 12, so y = 6. The y-intercept is (0, 6).
First calculate the slope using m = (y₂ − y₁) / (x₂ − x₁). Then use the point-slope formula y − y₁ = m(x − x₁) and set x = 0 to solve for y. The result is the y-intercept b = y₁ − m·x₁.
In slope-intercept form y = mx + b, the y-intercept is simply the value of b. No calculation is required — b is the value of y when x equals zero, and it directly tells you where the line crosses the y-axis. You might also find our calculate Absolute Value Inequality Solver Solution Interval useful.
No, a straight line can have at most one y-intercept. Since a linear function passes through each x-value exactly once, it can only cross the y-axis at a single point. Vertical lines (x = c) are an exception — they never cross the y-axis unless c = 0.
The y-intercept is where the line crosses the y-axis (x = 0), while the x-intercept is where the line crosses the x-axis (y = 0). To find the x-intercept, set y = 0 in the equation and solve for x. Both intercepts together can help you graph a line quickly.
A frequent mistake is confusing the slope m with the y-intercept b, especially when reading equations quickly. Another error is forgetting to rearrange equations into slope-intercept form before identifying b. Always ensure the equation is solved for y before reading off the intercept.
Yes — any function can have a y-intercept, found by evaluating f(0). For example, f(x) = x² + 3 has a y-intercept of 3. However, nonlinear functions may also have no y-intercept if f(0) is undefined, as in f(x) = 1/x or f(x) = ln(x).