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)

5

7.5

9

11

13

16


Which representation is **most** appropriate for displaying and describing what is happening to the amount of hot chocolate over time?

    

To display and describe the relationship between the time the hot chocolate machine is turned on and the amount of hot chocolate dispensed, the most appropriate representation would be a **line graph**. Here’s why:

1. **Visualizing Trends**: A line graph is excellent for showing trends over time. By plotting time (seconds) on the x-axis and the amount of hot chocolate (fluid ounces) on the y-axis, you can clearly see how the amount of hot chocolate increases as time progresses.
   
2. **Continuous Data**: The data in this scenario is continuous, meaning that the machine's operation and the amount of hot chocolate dispensed can be measured at any point in time. A line graph effectively represents continuous data.

3. **Identifying Patterns**: With a line graph, you can easily identify patterns or relationships between the two variables. For example, you can observe if the amount of hot chocolate increases at a constant rate or if there are any changes in the rate of increase over time.

Here’s a step-by-step guide on how to create a line graph for this dataTo display and describe the relationship between the time the hot chocolate machine is turned on and the amount of hot chocolate dispensed, the most appropriate representation would be a **line graph**. Here’s why:

1. **Visualizing Trends**: A line graph is excellent for showing trends over time. By plotting time (seconds) on the x-axis and the amount of hot chocolate (fluid ounces) on the y-axis, you can clearly see how the amount of hot chocolate increases as time progresses.
   
2. **Continuous Data**: The data in this scenario is continuous, meaning that the machine's operation and the amount of hot chocolate dispensed can be measured at any point in time. A line graph effectively represents continuous data.

3. **Identifying Patterns**: With a line graph, you can easily identify patterns or relationships between the two variables. For example, you can observe if the amount of hot chocolate increases at a constant rate or if there are any changes in the rate of increase over time.

Here’s a step-by-step guide on how to create a line graph for this 

1. **Label the Axes**: Label the x-axis as "Time (seconds)" and the y-axis as "Hot Chocolate Amount (fluid ounces)".
2. **Plot the Data Points**: Plot each pair of values (time, amount) as a point on the graph.
3. **Draw the Line**: Connect the points with a line to show the trend.

Here is the data to be plotted:
- At 4 seconds, 5 fluid ounces
- At 8 seconds, 7.5 fluid ounces
- At 12 seconds, 9 fluid ounces
- At 16 seconds, 11 fluid ounces
- At 20 seconds, 13 fluid ounces
- At 24 seconds, 16 fluid ounces

Using a line graph will clearly show the relationship between the time the machine is on and the amount of hot chocolate dispensed.

Would you like more details or have any questions?

Here are some additional questions you might want to explore:
1. How can you determine if the relationship between time and amount of hot chocolate is linear?
2. What other types of graphs could be used to represent this data?
3. How would you calculate the rate at which the hot chocolate is dispensed?
4. Can you use this data to predict the amount of hot chocolate dispensed at 30 seconds?
5. What are the advantages and disadvantages of using a line graph for this data?

**Tip:** When interpreting data from graphs, always check the scale and units on both axes to understand the relationship correctly.

Explore how the amount of hot chocolate dispensed changes over time using a line graph. Learn to plot and interpret the relationship between time (seconds) and hot chocolate amount (fluid ounces). Suitable for Grades 6-8.

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