X And Y Intercept Calculator

What this calculator does

So, you have a straight line and you want to know where it crosses the axes. This tool finds the x-intercept and the y-intercept, and it tells you the slope along the way. You can describe your line in any of five ways, and it works out the crossing points from whichever you choose.

A dropdown selects how you want to enter the line, and the input boxes change to match.

How to use it

1. Choose how you will describe the line from the dropdown.
2. Enter the values that method needs, whether points, a slope, or equation coefficients.
3. Press Calculate.

What the intercepts are

The intercepts are the points where a line crosses the two axes. The x-intercept is where the line crosses the horizontal x-axis, and the y-intercept is where it crosses the vertical y-axis. These two points are natural landmarks for any line: the y-intercept tells you where the line starts as it passes the vertical axis, and the x-intercept tells you where it hits zero on the way across. Together they make a line easy to picture and quick to sketch.

Finding them by setting a variable to zero

There is a clean rule for finding either intercept. On the x-axis, the y value is always zero, so to find the x-intercept you set y to zero and solve for x. On the y-axis, the x value is always zero, so to find the y-intercept you set x to zero and solve for y. That is the whole idea: each axis is defined by one coordinate being zero, and setting that coordinate to zero pins down where the line meets it. The tool does this from whatever description of the line you give it.

Five ways to describe the line

A line can be specified in several equivalent ways, and the tool accepts five of them. You can give two points that the line passes through. You can give one point and the slope. You can give the slope and the y-intercept, the slope-intercept form. You can give the point-slope form directly. Or you can give the standard form, an equation of the shape A times x plus B times y equals C. Whichever you pick, the underlying line is the same, so the intercepts come out the same. This flexibility means you can use whatever information you happen to have.

A worked example

Take the line described by a slope of 2 and a y-intercept of minus 4, which is the equation y equals 2x minus 4. To find the x-intercept, set y to zero: 0 equals 2x minus 4, so 2x is 4 and x is 2, giving the point 2 comma 0. The y-intercept is where x is zero, which is minus 4, giving 0 comma minus 4. So the line crosses the x-axis at 2 comma 0 and the y-axis at 0 comma minus 4, with a slope of 2.

Horizontal and vertical lines

Two kinds of line need special handling, and the tool takes care of them. A horizontal line never crosses the x-axis unless it lies on it, since it stays at a fixed height, so it has a y-intercept but no ordinary x-intercept. A vertical line is the reverse: it crosses the x-axis at one place but never meets the y-axis, and its slope is undefined because it has no run. The tool reports these cases honestly rather than forcing a number where none exists. For the perpendicular partner of a line, the perpendicular line calculator handles that.

Questions people ask

What are the x and y intercepts?

The points where a line crosses the axes: the x-intercept on the horizontal axis, the y-intercept on the vertical axis.

How are they found?

Set y to zero and solve for x to get the x-intercept; set x to zero and solve for y to get the y-intercept.

What ways can I enter the line?

Five: two points, a point and slope, slope and y-intercept, point-slope form, or standard form.

Does it give the slope too?

Yes. Along with the two intercepts, it reports the slope of the line.

What about horizontal or vertical lines?

A horizontal line has no x-intercept and a vertical line has no y-intercept and an undefined slope. The tool reports these rather than inventing a value.

References

On intercepts. The x-intercept is where a line meets the x-axis, and the y-intercept is where it meets the y-axis.

1. Eric W. Weisstein, "x-Intercept," from MathWorld, a Wolfram resource, on the point where a curve crosses the x-axis, where y is zero.
2. Eric W. Weisstein, "y-Intercept," from MathWorld, a Wolfram resource, on the point where a curve crosses the y-axis, where x is zero.