Question

Is it possible for a line to have no x-intercept?

Answer 1

Yes if the line has the equation y = 0x + b

Explanation:

A line with a slope of zero ( O) will be parallel to the x axis. The line will pass through the y axis at the point (0,b). The line will never pass through the x axis.

Answer 2

Yes. A line parallel to the x-axis (slope of 0) will never intersect it.

Explanation:

For this question, I'll assume you're talking about a normal linear function (a polynomial with a degree of 0 or 1).

Since we know that the line will go on infinitely, if it has any slant at all it will eventually intersect one of the axes.

However, some lines have no slant at all. If a line is parallel to one of the axes, then it will never intersect that axis. Take the equation y=-2:

graph{y=(0x)-2 [-10, 10, -5, 5]}

The x-axis is defined by the equation y=0x+0. Since we see that our equation and that of the x-axis have the same slope, they will never intersect.

So, to answer your question, any equation of the form y=b will have no x-intercept, except y=0, which will have infinitely many intercepts.

The same can be true of lines that have no y-intercept, but their slope is undefined and you can graph them with the formula x=b instead.