Final answer:
In this case, Rachel's distance from home increases at a constant rate of 4 meters per second. The relationship between her distance, y, and the time she takes to cycle, x, can be represented by the equation y = 4x + 6.
Step-by-step explanation:
Rachel's distance from home, y meters, is a function of the time she takes to cycle, x seconds. From the table given, we can observe that as the time increases, Rachel's distance from home also increases.
To determine the rate at which Rachel is cycling, we can look at the change in distance divided by the change in time. In this case, the change in distance is 4 meters (from 6 to 10) and the change in time is 1 second (from 0 to 1). Therefore, Rachel is cycling at a rate of 4 meters per second.
Using this information, we can determine Rachel's distance from home at any given time. For example, if Rachel cycles for 10 seconds, her distance from home can be calculated as follows:
- Change in distance = rate × change in time
- Change in distance = 4 meters/second × 10 seconds = 40 meters
Therefore, Rachel's distance from home after 10 seconds of cycling would be 40 meters.
In general, we can write the relationship between Rachel's distance from home, y, and the time she takes to cycle, x, as a linear equation:
y = mx + b
where m represents the rate of cycling and b represents the initial distance from home (when x = 0).
From the given table, we can see that when x = 0, y = 6. Therefore, the equation becomes:
y = 4x + 6
This equation allows us to calculate Rachel's distance from home at any given time. For example, when x = 3, we can substitute it into the equation:
- y = 4(3) + 6
- y = 12 + 6
- y = 18
So, after 3 seconds of cycling, Rachel's distance from home would be 18 meters.
In summary, Rachel's distance from home increases at a constant rate of 4 meters per second. The relationship between her distance, y, and the time she takes to cycle, x, can be represented by the equation y = 4x + 6. This equation allows us to calculate Rachel's distance from home at any given time.
Your question is incomplete, but most probably the full question was:
Rachel starts cycling a distance away from her house at a constant rate. The table shows her distance from home, y meters, as a function of the time she takes to cycle, x seconds.
| x (seconds) | 0 | 1 | 2 | 3 | 4 | 5 |
| y (meters) | 6 | 10| 14| 18| 22| 26|
Determine her constant rate of cycling and the relationship between her distance, y, and the time she takes to cycle, x.