To determine the correct statements based on the given information that the relationship between the height of a plant and the time is linear, we need to understand the concept of the rate of change. The rate of change in a linear relationship, also known as the slope, represents the amount by which the dependent variable (in this case, the plant's height) changes for a one-unit change in the independent variable (time in weeks).
Assuming you have a graph showing this relationship, here's how you can verify the correct statements:
1. **The rate of change is 4.**
2. **The rate of change is 1.**
3. **The rate of change is .**
4. **The plant grows 4 cm in 1 week.**
5. **The plant grows 1 cm in 4 weeks.**
From a linear graph, you typically find the rate of change (or slope) by observing how much the height changes for each unit change in time. However, let's analyze each statement without having the actual slope calculated from a graph:
- **The rate of change is 4.**
This would mean that for each increase of 1 week, the height of the plant increases by 4 cm.
- **The rate of change is 1.**
This would mean that for each increase of 1 week, the height of the plant increases by 1 cm.
- **The rate of change is .**
This seems incomplete and likely a mistake as rates of change are numerical values.
- **The plant grows 4 cm in 1 week.**
This is equivalent to stating that the rate of change is 4, confirming the same relationship.
- **The plant grows 1 cm in 4 weeks.**
This translates to a rate of change of 1/4 (0.25) cm per week.
Thus, if there was an actual graph available, you would check how much the height increases as the weeks increase to find the correct rate of change. For example, if after 1 week the plant grows by 4 cm, the statements about the rate of change being 4 and the plant growing 4 cm in 1 week would be correct.
If after 4 weeks the plant has grown only 1 cm, then the rate of change is 1/4 cm per week, confirming the plant grows 1 cm in 4 weeks statement.
However, without the actual graph or further information to confirm which slope is correct, the analysis tells us to focus on consistent information translation.
So, the statements that are likely correct based on typical rate interpretation are:
- **The plant grows 4 cm in 1 week.** - if the slope indicates an increase of 4 cm per week.
- **The rate of change is 4.** - if the slope is 4 cm per week.
If you have the specific data points from the graph, you should use them to determine the slope directly to confirm the above verification.
The graph shows the linear relationship between the height of a plant (in centimeters) and the time (in weeks) that the plant has been growing.
Which statements are correct? Check all that apply.
The rate of change is 4.
The rate of change is 1.
The rate of change is .
The plant grows 4 cm in 1 week.
The plant grows 1 cm in 4 weeks.
1 answer