(b)**** Find the equation of the line containing the first and the last data points.

To find the equation of the line that contains the first and last data points, we will use the coordinates \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (8, 15)\).

The equation of a line in slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, calculate the slope \( m \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - 3}{8 - 2} = \frac{12}{6} = 2
\]

Now that we have the slope \( m = 2 \), we can use one of the points to find the y-intercept \( b \). Using the point \((2, 3)\):

\[
y = mx + b \\
3 = 2(2) + b \\
3 = 4 + b \\
b = 3 - 4 \\
b = -1
\]

Therefore, the equation of the line is:

\[
y = 2x - 1
\]

Would you like details or have any questions? Here are 5 questions you might want to ask:
1. How do you find the slope of a line given two points?
2. What is the significance of the y-intercept in the equation of a line?
3. How can we verify that the line equation is correct?
4. What are other forms of the equation of a line?
5. How do you plot the line equation on a scatter plot?

**Tip**: When calculating the slope, ensure that you subtract the y-coordinates and x-coordinates in the correct order to avoid sign errors.

Learn how to find the equation of a line that passes through the points (2, 3) and (8, 15) using the slope formula and slope-intercept form. This problem covers coordinate geometry and linear equations. Suitable for students in Grades 7-9.

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