Question
Baristas at Hot Cocoa Coffee Shop tested their new hot chocolate machine. The following table shows the number of seconds the machine was turned on and the amount of hot chocolate that filled up the cup.
Time (seconds) 4 8 12 16 20 24
Hot Chocolate Amount (fluid ounces) 4 5.5 7 9 12 15
Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?
scatter plot titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 4 and 8 comma 5 and a half and 12 comma 7 and 16 comma 9 and 20 comma 12 and 24 comma 15
line graph titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 4 and 8 comma 5 and a half and 12 comma 7 and 16 comma 9 and 20 comma 12 and 24 comma 15, with line segments connecting each point to the next
scatter plot titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 4 comma 4, 5.5 comma 8, 7 comma 12, 9 comma 16, 12 comma 20, and 15 comma 24
Time (seconds) 4 8 12 16 20 24
Hot Chocolate Amount (fluid ounces) 4 5.5 7 9 12 15
Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?
scatter plot titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 4 and 8 comma 5 and a half and 12 comma 7 and 16 comma 9 and 20 comma 12 and 24 comma 15
line graph titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 4 and 8 comma 5 and a half and 12 comma 7 and 16 comma 9 and 20 comma 12 and 24 comma 15, with line segments connecting each point to the next
scatter plot titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 4 comma 4, 5.5 comma 8, 7 comma 12, 9 comma 16, 12 comma 20, and 15 comma 24
Answers
GPT-4o mini
The most appropriate representation for displaying and describing the relationship between the amount of hot chocolate and the time the machine was turned on is a **line graph titled "New Machine"**.
Here's why:
- **Continuous Relationship**: The relationship between time and the amount of hot chocolate is continuous, as the hot chocolate amount increases over time in a consistent manner. A line graph effectively illustrates this type of relationship, showing how the amount of hot chocolate filled in the cup changes over the seconds.
- **Connecting Points**: The line graph includes line segments connecting each point to the next, which visually emphasizes the trend and allows for easier interpretation of changes over time.
- **Axes Orientation**: In this case, the x-axis (time in seconds) is appropriate for the independent variable (time), while the y-axis (hot chocolate amount in fluid ounces) is appropriate for the dependent variable (amount of hot chocolate).
The other options (scatter plot with time on the x-axis and amounts on the y-axis or scatter plot with amounts on the x-axis and time on the y-axis) do not communicate the continuous nature of the relationship as effectively as the line graph does.
### Summary:
The **line graph** is the best representation to illustrate the continuous increase in the amount of hot chocolate over the time the machine was on.
Here's why:
- **Continuous Relationship**: The relationship between time and the amount of hot chocolate is continuous, as the hot chocolate amount increases over time in a consistent manner. A line graph effectively illustrates this type of relationship, showing how the amount of hot chocolate filled in the cup changes over the seconds.
- **Connecting Points**: The line graph includes line segments connecting each point to the next, which visually emphasizes the trend and allows for easier interpretation of changes over time.
- **Axes Orientation**: In this case, the x-axis (time in seconds) is appropriate for the independent variable (time), while the y-axis (hot chocolate amount in fluid ounces) is appropriate for the dependent variable (amount of hot chocolate).
The other options (scatter plot with time on the x-axis and amounts on the y-axis or scatter plot with amounts on the x-axis and time on the y-axis) do not communicate the continuous nature of the relationship as effectively as the line graph does.
### Summary:
The **line graph** is the best representation to illustrate the continuous increase in the amount of hot chocolate over the time the machine was on.