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To find the equation of the linear function in slope-intercept form \( y = mx + b \), we need to determine two key components:

1. **Slope \( m \) (rate of change)**: The slope can be calculated by taking any two points \((x_1, y_1)\) and \((x_2, y_2)\) from the table and using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

2. **Intercept \( b \) (y-intercept)**: Once we know the slope, we can substitute a point \((x_1, y_1)\) into the slope-intercept equation to solve for \( b \).

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

Using the points \((-1, 6)\) and \((3, -6)\) from the table:
\[
m = \frac{-6 - 6}{3 - (-1)} = \frac{-12}{4} = -3
\]

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

Now that we know \( m = -3 \), use one of the points to find \( b \). Let's use the point \((-1, 6)\):
\[
y = mx + b \implies 6 = -3(-1) + b \implies 6 = 3 + b
\]
\[
b = 6 - 3 = 3
\]

### Final Equation
The equation of the linear function is:
\[
y = -3x + 3
\]

Would you like more details on this process or explanations of any specific steps?

Here are 5 related questions for further practice:
1. How do you find the slope if the table has more points?
2. What is the meaning of a negative slope in a linear equation?
3. How do you interpret the y-intercept graphically?
4. Can you find the equation using other pairs of points from the table?
5. How would you graph the equation \( y = -3x + 3 \)?

**Tip:** The slope tells you how much \( y \) changes for a given change in \( x \), and it can be understood as the "steepness" of the line.

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 using a table of values in slope-intercept form. This problem covers key algebraic concepts such as slope calculation and identifying the y-intercept. Suitable for students in Grades 7-9.

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