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To find the equation of the linear function from the given table, we need to write the equation in slope-intercept form, which is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept (the value of \(y\) when \(x = 0\)).

### Step 1: Find the slope (\(m\))
The slope \(m\) is the rate of change of \(y\) with respect to \(x\), which can be calculated as:

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

From the table, pick any two points. Let's take the points \((x_1, y_1) = (0, -4)\) and \((x_2, y_2) = (1, 2)\).

\[
m = \frac{{2 - (-4)}}{{1 - 0}} = \frac{2 + 4}{1} = \frac{6}{1} = 6
\]

So, the slope \(m = 6\).

### Step 2: Find the y-intercept (\(b\))
From the table, we can see that when \(x = 0\), \(y = -4\). Therefore, the y-intercept \(b = -4\).

### Final Equation
Now that we know the slope and the y-intercept, the equation of the line is:

\[
y = 6x - 4
\]

You can now enter this as the equation for the linear function.

Do you need further clarification or details? Here are some related questions:

1. What is the general form of a linear equation?
2. How can you determine the slope of a line from a table?
3. What does the y-intercept represent in a real-world context?
4. How do you verify if a table represents a linear function?
5. Can we derive a linear equation using different pairs of points?

**Tip:** Always choose two clear points from the table to calculate the slope accurately.

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

Table:
| x | 0 | 1 | 2 | 3 | 4 |
| y | -4 | 2 | 8 | 14 | 20 |

Learn how to find the equation of a linear function in slope-intercept form based on a table of values. This example uses points (0, -4) and (1, 2) to calculate the slope and determine the equation of the line. Suitable for students in Grades 7-9.

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