The x- and y-intercepts occur when the function crosses the x- and y-axes, respectively. At the x-intercept, y is 0. Similarly, at the y-intercept, x is 0. We can identify these coordinate pairs in the given table,
Position of Scuba Diver
Time (s), x
Depth (m), y
0
- 24
3
- 18
6
- 12
9
- 6
12
0
We can see that when x=0, y=- 24. This means that our y-intercept is - 24. We can also see that when y=0, x=12, meaning that our x-intercept is 12.
Interpreting the Intercepts
The table involves a diver's depth as a function of time. The y-intercept tells us that when their position is first measured at 0 seconds, the diver is at a depth of 24 meters. The x-intercept tells us how long it took the diver to surface. We know that after 12 seconds have passed, the diver's depth is 0 meters, which suggests that it took them 12 seconds to surface.
Intercept
Interpretation
(0,-24)
The diver starts at a depth of 24 meters.
(12,0)
The diver surfaces after 12 seconds.
By the way, if you are ever scuba diving, DO NOT surface this fast or you can badly hurt yourself!
