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To find the equation of the linear function in slope-intercept form (\(y = mx + b\)) using the given table, we follow these steps:

### Step 1: Find the slope (\(m\))
The slope (\(m\)) is the rate of change of \(y\) with respect to \(x\). Use the formula:

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

Select two points from the table, such as \((-1, -2)\) and \((2, 10)\):

\[
m = \frac{10 - (-2)}{2 - (-1)} = \frac{10 + 2}{2 + 1} = \frac{12}{3} = 4
\]

### Step 2: Solve for the y-intercept (\(b\))
Using the slope (\(m = 4\)) and one point, substitute into \(y = mx + b\). Use the point \((2, 10)\):

\[
10 = 4(2) + b
\]

\[
10 = 8 + b \implies b = 2
\]

### Step 3: Write the equation
Substitute \(m = 4\) and \(b = 2\) into \(y = mx + b\):

\[
y = 4x + 2
\]

### Final Answer:
The equation of the linear function is:

\[
y = 4x + 2
\]

Let me know if you want further details or have any questions!

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Here are 5 related questions to explore:
1. How can you verify the slope using different pairs of points from the table?
2. How does changing one of the \(y\)-values in the table affect the equation of the line?
3. What would the graph of \(y = 4x + 2\) look like?
4. Can you find the \(x\)-intercept of the line?
5. How can this method be extended to find the equation of a nonlinear function?

**Tip:** Always double-check your slope calculation using multiple pairs of points to confirm consistency.

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

Learn how to determine the equation of a linear function in slope-intercept form using a given table of values. This example explores concepts like calculating slope and finding the y-intercept, ideal for students in Grades 8-10.

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