The problem asks to create a linear model for the data given in the table. We can write a linear equation in the form:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

We can calculate the slope $m$ using the formula:

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

Let's take two points from the table. For instance, the points $(2, 5)$ and $(6, 11)$:

$m = \frac{11 - 5}{6 - 2} = \frac{6}{4} = 1.5$

So, the slope $m = 1.5$.

Next, we use the slope-intercept form to find the y-intercept $b$. Using the point $(2, 5)$:

$5 = 1.5(2) + b$ $5 = 3 + b$ $b = 5 - 3 = 2$

Thus, the linear model is:

$y = 1.5x + 2$

Would you like more details or have any questions? Here are some related questions you might find useful:

1. What is the method to calculate the slope if only two points are provided?
2. How do you verify if a set of points follows a linear model?
3. Can you create a different linear model using other pairs of points from the table?
4. What is the significance of the slope in a linear model?
5. How does the y-intercept affect the graph of the equation?

Tip: When calculating a linear model from data, always use more points to ensure consistency in your slope and intercept.