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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.

Create a linear model for the data in the table. x: [2, 6, 9, 10, 11, 13, 17], y: [5, 11, 14, 16, 18, 21, 27]

Learn how to create a linear model from data points. This exercise covers calculating the slope and y-intercept to form a linear equation, suitable for students in Grades 8-10.

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