A line with only an x-intercept is a line of the form x=a, where a≠0. These are known as vertical lines. The line x=1 does not have any y-intercepts but has exactly one x-intercept.
Exactly 2 x-intercepts
This is impossible. Lines are straight, and cannot bend or change direction. Therefore, no line can cross the x-axis twice.
No x-intercept, One y-intercept
A line with no x-intercept is a horizontal line of the form y=a, where a≠0. An example of this is shown below.
Exactly 2 y-intercepts
This is impossible for the same reason a line cannot have two x-intercepts.
b Let's consider our results from Part A.
It is possible to draw a line that has one x-intercept and one y-intercept. Any line with a positive or negative slope will do it.
It is also possible to draw a line with only one x-intercept and no y-intercept. Any vertical line that does not coincide with the y-axis will work.
It is not possible to draw a line with exactly two x-intercepts. Only a curve will satisfy such a condition.
It is also possible to draw a line with only one y-intercept and no x-intercept. Any horizontal line that does not coincide with the y-axis will work.
It is not possible to draw a line with exactly two y-intercepts. Only a curve such as the one below will satisfy such a condition.
c When a line is drawn in a coordinate system it can have at most one intercept per axis. In fact, a line must intercept at least one of the axes.
