Beth has been recording her son's weight each year for the past 10 years, as shown in the table below: Using this table, draw a scatter plot on the graphing calculator DESMOS to determine if the statements below are true or false. (3 points) True False The data suggests a linear association between the recorded age and weight. The data can be represented with a line of best fit y=5x+15 There is no correlation between the recorded age and weight.

To determine whether the statements are true or false based on Beth's recorded data, you will need to plot the data points and analyze the scatter plot. Here’s how to do that step-by-step on the graphing calculator DESMOS:

1. Input the Data: First, you'll need to enter the data points into DESMOS. The data you have corresponds to:

   • Age (x): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
   • Weight (y): 21, 28, 31, 35, 40, 46, 51, 57, 64, 71

   Input the data points as follows:

   (1, 21), (2, 28), (3, 31), (4, 35), (5, 40), (6, 46), (7, 51), (8, 57), (9, 64), (10, 71)
   

2. Create the Scatter Plot: Once you have the data points inputted, DESMOS will automatically create a scatter plot from these coordinates.

3. Examine the Scatter Plot:

   • Look for a pattern in the data points. If the points seem to align closely or trend in a straight line, this suggests a linear association.
   • If the data points do not show any clear trend or pattern, it may suggest there is no correlation.

4. Evaluate each statement:

   • Statement 1: "The data suggests a linear association between the recorded age and weight."

     • Based on the scatter plot, if you see that the points roughly form a straight line, this statement is True.

   • Statement 2: "The data can be represented with a line of best fit y=5x+15."

     • To check this, you can add the line of best fit in DESMOS by inputting y = 5x + 15. Analyze how well this line fits the data points. If it aligns closely with the points, this statement is True; if it only fits a few points and misses many others, it would be False.

   • Statement 3: "There is no correlation between the recorded age and weight."

     • If there is a linear association, as observed from Statement 1, this statement would be False.

After you analyze the scatter plot and check the line of best fit in DESMOS, you should be able to definitively classify each statement as True or False.

Conclusion:

1. If the scatter plot shows a linear trend:

   • Statement 1: True
   • Statement 2: Depending on fit: True if it fits well, False otherwise.
   • Statement 3: False

2. If the scatter plot does not show a linear trend:

   • Statement 1: False
   • Statement 2: False
   • Statement 3: True

By following these steps, you should be able to effectively assess the statements based on the scatter plot you generate.