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To solve this problem, we need to create a linear model using the data from Pax and Snowflake, then determine which dolphin's weight deviates the most from the predicted weight based on this model.

### Step 1: Create the Linear Model
We start by finding the linear equation \( y = mx + b \), where:
- \( y \) is the weight (in pounds).
- \( x \) is the length (in feet).
- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

Given points for Pax \((7.6, 519)\) and Snowflake \((8.2, 549)\), we calculate the slope \( m \) using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{549 - 519}{8.2 - 7.6}
\]

Let's calculate the slope \( m \).The slope \( m \) of the linear model is approximately 50.

### Step 2: Find the y-intercept \( b \)
Using the point for Pax \((7.6, 519)\) and the slope \( m = 50 \), we use the formula:

\[
y = mx + b \implies 519 = 50 \times 7.6 + b
\]

Let's calculate the intercept \( b \).The y-intercept \( b \) of the linear model is approximately 139.

### Step 3: Form the Linear Equation
The linear equation of the model is:

\[
y = 50x + 139
\]

### Step 4: Predict the Weights of Each Dolphin
Now, let's use this equation to predict the weights of each dolphin and determine which dolphin's weight deviates the most from the predicted value. We will calculate the predicted weights and the differences for each dolphin.The deviations of the dolphins' weights from the predicted values are:

- Snowflake: 0.0 lbs
- Shadow: 8.0 lbs
- Corky: 2.0 lbs
- Pax: 0.0 lbs
- JoJo: 31.0 lbs
- Blaze: 9.0 lbs

The dolphin whose weight differs the most from the value predicted by the model is **JoJo**, with a deviation of 31 lbs.

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you determine the slope and intercept of a linear equation using two points?
2. What are some other methods to evaluate the accuracy of a linear model?
3. How do outliers affect a linear regression model?
4. Can we use other points besides Pax and Snowflake to improve the model?
5. How would the model change if we used all dolphins' data points?

**Tip:** When creating a linear model, always check if the chosen data points accurately represent the overall trend to avoid skewed results.

The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). Which dolphin’s weight differs most from the value predicted by this model?

Create a linear model to predict the weight of dolphins based on their length using data from Pax and Snowflake. Learn how to find the slope and y-intercept, and determine which dolphin's weight deviates the most from the predicted value.

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