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The table provided lists the values for \( x \) and \( y \), which we can use to determine the linear equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Given dataThe table provided lists the values for \( x \) and \( y \), which we can use to determine the linear equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Given 
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 2 \\
2 & 4 \\
4 & 6 \\
\end{array}
\]

### Step 1: Calculate 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 points \( (0, 2) \) and \( (2, 4) \):
\[
m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1
\]

### Step 2: Determine the y-intercept (\( b \))
Since the y-intercept is where \( x = 0 \), from the table, when \( x = 0 \), \( y = 2 \). Therefore, \( b = 2 \).

### Step 3: Write the equation
Now that we have the slope \( m = 1 \) and the y-intercept \( b = 2 \), the equation is:
\[
y = 1x + 2 \quad \text{or simply} \quad y = x + 2
\]

Thus, the equation of the linear function is \( y = x + 2 \).

Would you like any further details or explanations on this process?

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Here are 5 related questions to expand on this concept:

1. How would you find the equation if the slope was a negative value?
2. What happens to the graph of a line if the y-intercept is 0?
3. Can a table represent a non-linear function? How can you tell from the values?
4. How would you solve for \( x \) given a specific value for \( y \) in this equation?
5. How can you use this equation to predict \( y \)-values for any \( x \)-value?

**Tip**: When working with a table, check if the change in \( y \) is consistent for equal changes in \( x \) to confirm it's a linear function.

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 in slope-intercept form based on a table of values. This tutorial walks through calculating the slope and y-intercept step-by-step. Suitable for students in Grades 8-10.

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