In graphing, we always talk about the x-intercept and the y-intercept. According to Seward (2011), intercepts are special types of solutions to algebraic equations. Intercepts may also be regarded as intersects or locations where the graph crisscrosses the x-axis or y-axis. The x-intercept is where the graph crosses the x-axis while the y-intercept is where the graph crosses the y-axis (Seward, 2011).
Based on the above descriptions, the value of y will always be 0 regardless of where one is on the x-axis. Similarly, the value of x will always be 0 at any point along the y-axis. The graph in figure 1 below shows the x and y-intercepts.
The x-intercept is the point (2, 0) along the x-axis and the y-intercept is the point (0, 3) along the y-axis. It is important to note that the x and y-intercepts are two separate points on the graph and the only time when both the x and y-intercepts will be the same is at point (0, 0) which is the origin.
Looking at the graph in figure 1, when a line does not have a y-intercept, it means that is a vertical line parallel to the y-axis. The line only crosses the x-axis and the value of x is a constant. This is illustrated by figure 2.
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