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To find the equation of the linear function, we need to determine both the slope (\( m \)) and the y-intercept (\( b \)) of the line. Here’s how we can solve it:

### Step 1: Determine the Slope (\( m \))
The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((0, 4)\) and \((1, 6)\) from the table:
\[
m = \frac{6 - 4}{1 - 0} = \frac{2}{1} = 2
\]

So, the slope \( m = 2 \).

### Step 2: Identify the Y-intercept (\( b \))
The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, we see that when \( x = 0 \), \( y = 4 \). Therefore, the y-intercept \( b = 4 \).

### Step 3: Write the Equation of the Line
The equation of a linear function in slope-intercept form is:
\[
y = mx + b
\]
Substituting the values of \( m = 2 \) and \( b = 4 \):
\[
y = 2x + 4
\]

### Answer Summary
- **Slope**: \( 2 \)
- **Y-intercept**: \( 4 \)
- **Equation**: \( y = 2x + 4 \)

Would you like more details or have any questions?

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Here are five related questions that could help deepen your understanding:
1. How would the equation change if the slope were different?
2. How can we determine the slope if only one point and the y-intercept are given?
3. How do we know if a function is linear from just a table of values?
4. What happens to the y-intercept if all values of \( y \) are increased by a constant?
5. How can we verify that all points in the table lie on the line \( y = 2x + 4 \)?

**Tip:** Always check multiple pairs of points to confirm the slope is consistent across a table for a linear function.

A table of values of a linear function is shown. Find the slope and y-intercept of the function's graph, and find the equation for the function.

Learn how to find the slope and y-intercept of a linear function given a table of values. Using the points (0, 4) and (1, 6), determine the slope as 2, and find the equation y = 2x + 4. Suitable for students in Grades 7-9.

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