To create a linear model for the data in the table, we need to find the equation of the form:

$y = mx + b$

where $m$ is the slope of the line, and $b$ is the y-intercept.

Step 1: Calculate the slope $m$

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let’s pick two points from the data, say $(x_1, y_1) = (55, 66)$ and $(x_2, y_2) = (2020, 4545)$.

Substitute the values into the slope formula:

$m = \frac{4545 - 66}{2020 - 55} = \frac{4479}{1965} \approx 2.277$

So, the slope $m$ is approximately 2.277.

Step 2: Find the y-intercept $b$

We can now use the formula $y = mx + b$ and substitute one of the points, say $(55, 66)$, and the slope $m = 2.277$ to solve for $b$:

$66 = 2.277(55) + b$

$66 = 125.235 + b$

$b = 66 - 125.235 \approx -59.235$

Step 3: Write the linear model

Now that we have both the slope $m \approx 2.277$ and the y-intercept $b \approx -59.235$, the linear model is:

$y = 2.277x - 59.235$

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Would you like to see more details or verify this model with other points from the data? Here are some related questions for you:

1. How would you check if the linear model is a good fit for this data?
2. What is the significance of the slope in the linear model?
3. How would you interpret the y-intercept in this context?
4. What happens if you try to fit a quadratic model instead of a linear one?
5. How can you calculate the residuals for each data point?

Tip: Always plot the data and the linear model to visually confirm if the model fits well!