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We are asked to find the slope \( m \) of the linear function \( f \), use the table to find the \( y \)-intercept, and give an equation that defines \( f \). 

The table gives the following points:

\[
(-6, -23), (-4, -15), (-2, -7), (0, 1), (2, 9)
\]

### Step 1: Find the slope \( m \)
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Using the points \( (-6, -23) \) and \( (-4, -15) \):

\[
m = \frac{-15 - (-23)}{-4 - (-6)} = \frac{-15 + 23}{-4 + 6} = \frac{8}{2} = 4
\]

So, the slope \( m = 4 \).

### Step 2: Find the y-intercept
The y-intercept occurs when \( x = 0 \). From the table, when \( x = 0 \), \( f(x) = 1 \). Therefore, the y-intercept is \( 1 \).

### Step 3: Write the equation of the line
The general equation of a line is:

\[
f(x) = mx + b
\]

We already know \( m = 4 \) and the y-intercept \( b = 1 \). So the equation of the line is:

\[
f(x) = 4x + 1
\]

### Final Answer:
- Slope \( m = 4 \)
- Y-intercept = 1
- The equation of the line is \( f(x) = 4x + 1 \).

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you find the slope using two different points?
2. What is the significance of the y-intercept in a linear equation?
3. Can you verify the equation by plugging in other values from the table?
4. How does changing the slope affect the steepness of a line?
5. What happens to the graph of the line if the y-intercept changes?

**Tip:** Always check the equation by substituting different points from the table to ensure the accuracy of the equation.

A linear function f has the ordered pairs listed in the table. Find the slope m of the graph of f, use the table to find the y-intercept of the line, and give an equation that defines f.

Learn how to find the slope, y-intercept, and the equation of a linear function given a set of points from a table. This solution covers key concepts like the slope formula and the slope-intercept form, with step-by-step calculations. Suitable for students in Grades 8-10.

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