For the data given​ below, answer parts ​(a) through ​(f).
x
2
3
4
5
6
7
8
y
5
7
8
11
13
15
17
Find the equation of the line containing the first and the last data points.

To find the equation of the line containing the first and last data points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula for the equation of a line in slope-intercept form: \( y = mx + b \).

### Step 1: Identify the first and last data points
- First point: \((x_1, y_1) = (2, 5)\)
- Last point: \((x_2, y_2) = (8, 17)\)

### Step 2: Calculate the slope \(m\)
The slope \(m\) of a line passing through two points is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the values:

\[
m = \frac{17 - 5}{8 - 2} = \frac{12}{6} = 2
\]

### Step 3: Use point-slope form to find the equation
The equation of a line in point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Using the slope \(m = 2\) and the point \((2, 5)\), we get:

\[
y - 5 = 2(x - 2)
\]

### Step 4: Simplify to slope-intercept form
Simplify the equation:

\[
y - 5 = 2x - 4
\]

\[
y = 2x - 4 + 5
\]

\[
y = 2x + 1
\]

### Final equation:
The equation of the line containing the first and last data points is:

\[
y = 2x + 1
\]

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Learn how to find the equation of a line that passes through the first and last points (2, 5) and (8, 17). This problem covers algebraic concepts such as the slope formula and point-slope form. Suitable for students in Grades 8-10.

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