The table shows how y, the distance in kilometers that a sailboat travels, is related to x, the time in hours that the sailboat spends traveling.

Sailboat Travel
Time (hours) Distance (kilometers)
1 8
3 24
5 40
7 56
9 72
Which graph shows this relationship?

A.
A graph has numbers from 0 to 10 on the x-axis and 0 to 100 in increments of 10 on the y-axis. A straight line start from (8, 0) and passes through the points (3, 30) and (10, 80).

B.
A graph has numbers from 0 to 10 on the x-axis and 0 to 100 in increments of 10 on the y-axis. A straight line start from (0, 0) and passes through the points (4, 30) and (10, 72).

C.
A graph has numbers from 0 to 10 on the x-axis and 0 to 100 in increments of 10 on the y-axis. A straight line start from (8, 0) and passes through the points (5, 40), (8, 60) and (10, 72).

D.
A graph has numbers from 0 to 10 on the x-axis and 0 to 100 in increments of 10 on the y-axis. A straight line start from (0, 0) and passes through the points (5, 40) and (10, 80).

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 days ago

To identify the correct graph that represents the relationship between the time (x) and distance (y) for the sailboat travel, let's first analyze the data provided in the table:

| Time (hours) | Distance (kilometers) |
|--------------|-----------------------|
| 1 | 8 |
| 3 | 24 |
| 5 | 40 |
| 7 | 56 |
| 9 | 72 |

We can see that the relation between time and distance is linear. To find the slope (rate of travel), we can calculate the change in distance per hour traveled:

For every increase of 2 hours in time (from 3 hours to 5 hours, for example), the distance increases by 16 kilometers:

- From 1 hour to 3 hours: Change = 24 - 8 = 16 km for 2 hours
- From 3 hours to 5 hours: Change = 40 - 24 = 16 km for 2 hours
- From 5 hours to 7 hours: Change = 56 - 40 = 16 km for 2 hours
- From 7 hours to 9 hours: Change = 72 - 56 = 16 km for 2 hours

From this, we can deduce that the speed is consistent: 16 kilometers per 2 hours, which equals 8 kilometers per hour.

Using this information, we can start at the origin (0, 0) to visualize this on a graph:

1. For 1 hour: 8 km
2. For 3 hours: 24 km
3. For 5 hours: 40 km
4. For 7 hours: 56 km
5. For 9 hours: 72 km

The line representing this graph would start at (0, 0) and go through the points corresponding to the distances calculated, and it should stretch up to at least (9, 72).

Now, let's analyze the options:

- **Option : starts from (8, 0) which is incorrect since we start at (0, 0).
- **Option B**: also starts from (0, 0) but passes through (4, 30), which does not correspond to any of the data points.
- **Option C**: starts from (8, 0), which is again incorrect.
- **Option D**: starts at (0, 0) and goes up to (10, 80), but these points do not accurately reflect the distances at the given hours.

Based on the analysis, none of the options correctly represent the data provided. However, Option D is the closest, but it contains errors in distances.

If you need the exact graph showing distance per hour, it should definitely start at (0, 0) and accurately hit (1, 8), (3, 24), (5, 40), (7, 56), and (9, 72) distinctly without going to (4, 30) or starting from (8, 0).