What is another name for x-intercept?

Answer 1

roots, zeros, and solutions

Answer 2

An x-intercept is a point at which some function crosses the x-axis, which is the horizontal axis. The term is usually only used for straight lines, which have exactly one x-intercept, unless they're parallel to the horizontal axis. For other functions, "root" is the more common term.

If you know the slope (m) and the x-intercept (x0) of a straight line, then the equation of the line is:

y = m(x-x0)

You can also find the x-intercept easily if your line equation is in standard form, Ax + By = C: it's just x = C/A.

You can also follow this two-step process that works for any form of the equation:

1. Replace y with 0 whenever it occurs, and simplify.

2. Solve the resulting equation for x.

Horizontal lines don't have an x-intercept. They either coincide with the x-axis, or are parallel to it at a distance. In that case, when you try to apply this process, you'll be stuck on the second step, because it won't have an x to solve for (or, if using the x = C/A shortcut, A will be 0).

Imagine the line drawn on graph paper. Now imagine two perpendicular lines that intersect each other in the middle of your paper. Each of those is called a coordinate axes, and you have two of them: the x-axis and the y-axis. The x-axis runs horizontal (left to right), and the y-axis runs vertical (top to bottom).

The x-intercept is the point where your line crosses the x-axis on your drawing. It should come as no surprise that the y-intercept is the point where your line crosses the y-axis on your drawing.

Here's how you can find the x-intercept.

Suppose you have a line in slope-intercept form, y = mx + b

Then the x-intercept must be where the value of y is zero. So,

0 = mx + b,

-b = mx,

x = -b / m is the x-intercept.

Not all lines have an x-intercept. For instance, imagine any constant line, y = c, where c is any number. This is just a line parallel to the x-axis. Thus, if c isn't 0, your line won't have an x-intercept. If c is 0, then your line is the x-axis.

The above is true for straight lines of the form y = mx + b. However, there are other lines that can be drawn on a plane, not all of which are functions, with unique f:x→y mappings. For example, a line parallel to the y-axis can be described as x = c; just like how y = c, which is a function, describes a line parallel to the x-axis.