Question

Beth has been recording her son's weight each year for the past 10 years, as shown in the table below:
Age (years) | Weight (pounds)
1|21
2|28
3|31
4|35
5|40
6|46
7|51
8|57
9|64
10|71

Using this table, draw a scatter plot on the graphing calculator DESMOS to determine if the statements below are true or false.


True False
The data can be represented with a line of best fit y=5x+15


The data suggests a linear association between the recorded age and weight.


There is no correlation between the recorded age and weight.

Answer 1

To analyze the statements based on the data provided in the table, you can indeed use the scatter plot on a graphing calculator like Desmos. Below, I will guide you on how to interpret the scatter plot and assess each statement.

### 1. Drawing the Scatter Plot
In Desmos, you would input the Age (x-values) and Weight (y-values) as two lists. Your input will look like this:

```
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
W = [21, 28, 31, 35, 40, 46, 51, 57, 64, 71]
```

You can then create a scatter plot by plotting the points (A, W).

### 2. Evaluating the Statements

**Statement 1: The data can be represented with a line of best fit \(y = 5x + 15\)**

- **Explanation:** To check this, you can plot the line \(y = 5x + 15\) over the scatter plot. You may calculate a linear regression (or line of best fit) using the data points.
- **Evaluation:** After calculating or plotting the regression line, you'll likely find that the relationship between age and weight appears to increase but may not align perfectly with that equation, leading to the conclusion that this statement is **False**.

---

**Statement 2: The data suggests a linear association between the recorded age and weight.**

- **Explanation:** Looking at the scatter plot, you should determine if the points tend to cluster around a straight line.
- **Evaluation:** As you observe the scatter plot, you will see that weights do indeed increase as age increases, suggesting a linear trend. Therefore, this statement is **True**.

---

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

- **Explanation:** Correlation implies that as one variable increases, the other does as well.
- **Evaluation:** Since you've observed a trend where weight increases with age, there is clearly a correlation. Therefore, this statement is **False**.

### Summary of Assessments
1. **False**
2. **True**
3. **False**

This analysis can help validate the statements based on how the data behaves visually in the scatter plot.