Question

use the line of fit, ( y = 0.335x + 3.655 ), to predict how many meets are won if the swimmer practices for 21 hours next week. explain whether this is a valid prediction. options: 51.78 meets, this is not a valid prediction because the extrapolated value is not reasonable; 10.69 meets, this is not a valid prediction because the extrapolated value is not reasonable; 10.69 meets, this is valid because it is a reasonable prediction; 51.78 meets, this is valid because it is a reasonable prediction.

Explanation:

Step1: Identify the formula and input

We have the line of fit \( y = 0.335x + 3.655 \), where \( x \) is the practice time in hours and \( y \) is the number of meets won. We need to find \( y \) when \( x = 21 \).

Step2: Substitute \( x = 21 \) into the formula

Substitute \( x = 21 \) into \( y = 0.335x + 3.655 \):
\[

$$\begin{align*} y&=0.335\times21 + 3.655\\ &=7.035+ 3.655\\ &= 10.69 \end{align*}$$

\]

Step3: Analyze the prediction validity

From the graph (even though not fully visible, the practice hours on the x - axis seem to be in a reasonable range, and 21 hours is likely an extrapolation but the value of 10.69 meets is a reasonable number of meets (since the number of meets should be a positive number and 10.69 is a plausible value for meets won based on the linear model). So this is a valid prediction because it is a reasonable prediction.

Answer:

10.69 meets, this is valid because it is a reasonable prediction