An intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.

Because there are two axes on a coordinate plane, there can be a x-intercept, which is the point where the graph crosses the x-axis, or a y-intercept, which is the point where the graph crosses the y-axis.

When the linear function is used to represent a real-world situation, the intercepts have significant meaning in the context of the problem.

In the interactive below, you are given a graph that represents a linear function for a particular situation. Identify the x-intercept and y-intercept from the graph by locating the coordinates of the point where the graph crosses the x-axis and the y-axis, respectively. Match the best interpretation of each intercept by clicking and dragging the sentence from the Description Bank to the slot next to each graph.

Pause and Reflect

How can you distinguish between the x-intercept and the y-intercept from a graph?

Interactive popup. Assistance may be required.

Need a hint?

Which intercept corresponds with which axis? Interactive popup. Assistance may be required.

Check Your Answer

The x-intercept is the point where the graph crosses the x-axis (horizontal axis) and the y-intercept is the point where the graph crosses the y-axis (vertical axis).

Practice

Interpret both the x- and y-intercepts in the relationships shown in the graphs below.

1. The graph shown below represents the number of tickets that a theater must sell in order to reach $350 in revenue from ticket sales.
   

   

   Interactive popup. Assistance may be required.

   Need a hint?

   Identify the variable represented by the values on each axis by studying the axis labels. Interactive popup. Assistance may be required.

   Check Your Answer

   The x-intercept, (70, 0), shows that if the theater sells only adult tickets, they must sell 70 adult tickets in order to generate $350 in revenue.
   The y-intercept, (0, 140), shows that if the theater sells only children’s tickets, they must sell 140 children’s tickets in order to generate $350 in revenue.


2. A hiker is hiking down a canyon toward the canyon floor. Her height above the canyon floor as a function of time is shown in the graph below.

   

   Interactive popup. Assistance may be required.

   Need a hint?

   Identify the variable represented by the values on each axis by studying the axis labels. Interactive popup. Assistance may be required.

   Check Your Answer

   The x-intercept, (18, 0), shows that in 18 minutes, the height of the hiker above the canyon floor will be zero; in other words, the hiker will reach the canyon floor in 18 minutes.
   The y-intercept, (0, 360), shows that at time = 0 minutes, the hiker is 360 feet above the canyon floor.