Question
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.
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.
Answers
GPT-4o mini
To determine which statements are correct regarding the linear relationship between the height of a plant and the time it has been growing, let's consider the definition of the rate of change in a linear graph.
The rate of change is generally defined as the ratio of the change in height to the change in time. If the graph shows that the plant grows at a constant rate, then each statement can be evaluated based on that.
Given that the statements provided include rates of change, let's analyze them:
1. **The rate of change is 4.** - This statement would be correct if the plant grows 4 cm for every 1 week. If that is the case based on the graph, check if the slope is 4.
2. **The rate of change is 1.** - This would be correct if the slope indicates the plant grows 1 cm in every time unit (week). Again, check the graph to see if this is relevant.
3. **The rate of change is .** - Since the statement is incomplete, it is not possible to evaluate it and consider it as non-applicable.
4. **The plant grows 4 cm in 1 week.** - This statement is true if the graph indicates the height increases by 4 cm for each week. Confirm on the graph if this is true.
5. **The plant grows 1 cm in 4 weeks.** - This would only be accurate if the graph indicates growth that averages to this over that time span. If the plant grows consistently over time, this can also be checked against the graph.
Based on the general descriptions provided without specific graph details, if 4 cm growth in one week is indeed indicated, then both "The rate of change is 4." and "The plant grows 4 cm in 1 week." would be correct.
If the slope indicates otherwise, then you need to adjust which statements are accepted based on the graph itself.
The rate of change is generally defined as the ratio of the change in height to the change in time. If the graph shows that the plant grows at a constant rate, then each statement can be evaluated based on that.
Given that the statements provided include rates of change, let's analyze them:
1. **The rate of change is 4.** - This statement would be correct if the plant grows 4 cm for every 1 week. If that is the case based on the graph, check if the slope is 4.
2. **The rate of change is 1.** - This would be correct if the slope indicates the plant grows 1 cm in every time unit (week). Again, check the graph to see if this is relevant.
3. **The rate of change is .** - Since the statement is incomplete, it is not possible to evaluate it and consider it as non-applicable.
4. **The plant grows 4 cm in 1 week.** - This statement is true if the graph indicates the height increases by 4 cm for each week. Confirm on the graph if this is true.
5. **The plant grows 1 cm in 4 weeks.** - This would only be accurate if the graph indicates growth that averages to this over that time span. If the plant grows consistently over time, this can also be checked against the graph.
Based on the general descriptions provided without specific graph details, if 4 cm growth in one week is indeed indicated, then both "The rate of change is 4." and "The plant grows 4 cm in 1 week." would be correct.
If the slope indicates otherwise, then you need to adjust which statements are accepted based on the graph itself.