Every linear equation can be represented as a line. Let's take a look at an example line that represents some linear equation. First we will analyze a line with a nonzero slope.
On our graph we cannot see the x-intercept of a line. However, it does not mean that this line does not have an x-intercept. In fact, every line with a nonzero slope has both intercepts, because lines do not have endpoints. This means that at some point every line crosses the x-axis. Let's extend our graph a little bit.
Now we can see that the x-intercept of this line is at (-4,0). Therefore, since lines continue indefinitely in both directions, the graph of every linear equation with a nonzero slope has an x-intercept. However, let's analyze the case of a horizontal line — a line with a slope of 0.
Here, the line also continues indefinitely in both directions, but we move horizontally. This means that the value of y will always be constant and there will be no x-intercept. Therefore, not every linear equation has an x-intercept.
