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The problem asks to find the equation of the linear function represented by the table in slope-intercept form. The given table provides the following \( x \) and \( y \) values:

\[
\begin{array}{c|c}
x & y \\
\hline
1 & 7 \\
2 & 12 \\
3 & 17 \\
4 & 22 \\
\end{array}
\]

### Step 1: Find the slope \( m \)

The slope of a line can be found using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We can use two points from the table, say \( (1, 7) \) and \( (2, 12) \):
\[
m = \frac{12 - 7}{2 - 1} = \frac{5}{1} = 5
\]

### Step 2: Find the y-intercept \( b \)

The slope-intercept form of a linear equation is:
\[
y = mx + b
\]
We already know that \( m = 5 \). To find \( b \), we can substitute one of the points into the equation. Using \( (1, 7) \):
\[
7 = 5(1) + b
\]
\[
7 = 5 + b
\]
\[
b = 7 - 5 = 2
\]

### Step 3: Write the equation

The equation of the line is:
\[
y = 5x + 2
\]

This is the equation of the linear function in slope-intercept form.

Would you like further clarification or details?

### 5 Relative Questions:
1. How do we calculate the slope if the points are not in order?
2. Can the slope of a linear function be negative?
3. What does the y-intercept represent graphically?
4. How do we verify that the equation fits all the given points?
5. Can the slope-intercept form be rearranged to other forms, like standard form?

**Tip**: Always double-check the slope by using different pairs of points to ensure consistency.

Find the equation of the linear function represented by the table below in slope-intercept form.

Learn how to find the equation of a linear function from a table of values in slope-intercept form. The table includes points (1,7), (2,12), (3,17), and (4,22), and covers key algebraic concepts such as calculating slope and identifying the y-intercept.

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