Question

Describe a line that has no \(x\) -intercept.

Short answer

A line that has no x-intercept will be parallel to the x-axis and its equation will take the form \(y = c\), where \(c\) is a constant.

Step-by-step solution

Understand the basics of line intercepts

The line intercept is the point at which the line crosses an axis. If it crosses the x-axis, it is called an x-intercept; if it crosses the y-axis, it is called a y-intercept.

Define a line with no x-intercept

A line that does not cross the x-axis at any point is said to have no x-intercept. This means that the line is parallel to the x-axis. It could lie above or below the x-axis, depending on the situation.

Describe the line

Since such line is parallel to x-axis, its equation can be written in the form of \(y = c\), where \(c\) is the y-coordinate of the line. Plugging any real number value for \(c\) will give us an equation of line parallel to x-axis.