Find X and Y Intercepts of a Line

Enter Calculation

Coefficient A

Coefficient B

Constant C

For a line in standard form Ax + By = C

Results

X-Intercept

( 3, 0 )

where the line crosses the x-axis

Y-Intercept (0, y)	( 0, 2 )
Slope (m)	-0.667

What This Calculator Does

This tool finds the x-intercept and y-intercept of a straight line written in standard form, Ax + By = C. The x-intercept is the point where the line crosses the x-axis (where y = 0), and the y-intercept is where it crosses the y-axis (where x = 0). It also reports the slope of the line as a bonus.

How to Use It

Enter the three coefficients A, B, and C from your equation in standard form. If your line is given as 2x + 3y = 6, then A = 2, B = 3, and C = 6. Click calculate and the tool returns both intercept points and the slope.

The Formula Explained

To find the x-intercept, set y = 0 in the equation. This leaves Ax = C, so \(x = \frac{C}{A}\). To find the y-intercept, set x = 0, leaving By = C, so \(y = \frac{C}{B}\). The slope from standard form is \(m = -\frac{A}{B}\). Note that if A = 0 the line is horizontal and has no x-intercept; if B = 0 it is vertical and has no y-intercept.

$$\begin{gathered} \text{For } \text{A}x + \text{B}y = \text{C} \\[1.5em] \text{X-intercept} = \frac{\text{C}}{\text{A}}, \quad \text{Y-intercept} = \frac{\text{C}}{\text{B}}, \quad m = -\frac{\text{A}}{\text{B}} \end{gathered}$$

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The x-intercept lies on the horizontal axis (y = 0) and the y-intercept on the vertical axis (x = 0).

Worked Example

Take the line 2x + 3y = 6. The x-intercept is

$$x = \frac{C}{A} = \frac{6}{2} = 3$$

giving the point (3, 0). The y-intercept is

$$y = \frac{C}{B} = \frac{6}{3} = 2$$

giving the point (0, 2). The slope is

$$m = -\frac{A}{B} = -\frac{2}{3} \approx -0.667$$

Plotting the calculated x- and y-intercepts and connecting them traces the line.

FAQ

What if A or B is zero? A zero denominator means that intercept does not exist. A horizontal line (A = 0) never crosses the x-axis except trivially, and a vertical line (B = 0) never crosses the y-axis.

Can I use decimals or negatives? Yes. Enter any real numbers for A, B, and C; the calculator handles negatives and decimals.

How do I convert slope-intercept form to standard form? Rearrange y = mx + b into -mx + y = b, then scale so coefficients are convenient integers if desired.