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We are asked to find the equation of the linear function represented by the table in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

The given table of values is:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 4 \\
2 & 3 \\
3 & 2 \\
4 & 1 \\
\hline
\end{array}
\]

### Step 1: Find the slope \( m \)
The slope \( m \) of a linear function is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (1, 4) \) and \( (2, 3) \) from the table:
\[
m = \frac{3 - 4}{2 - 1} = \frac{-1}{1} = -1
\]
Thus, the slope \( m = -1 \).

### Step 2: Find the y-intercept \( b \)
To find \( b \), substitute the slope \( m = -1 \) and one of the points (e.g., \( (1, 4) \)) into the slope-intercept form \( y = mx + b \):
\[
4 = -1(1) + b
\]
\[
4 = -1 + b
\]
\[
b = 5
\]

### Step 3: Write the equation
Now that we have \( m = -1 \) and \( b = 5 \), the equation of the linear function is:
\[
y = -x + 5
\]

This is the required linear equation in slope-intercept form.

Would you like further details or have any questions? Here are some related questions for practice:

1. How would the equation change if the y-intercept were different?
2. Can you explain how to find the slope from any two points in general?
3. What happens to the line if the slope \( m \) were positive?
4. How can you verify if other points from the table satisfy the equation \( y = -x + 5 \)?
5. How do you graph the equation \( y = -x + 5 \)?

**Tip:** Always pick two different points from a table to calculate the slope of a linear function, ensuring consistency in results.

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

x | y
1 | 4
2 | 3
3 | 2
4 | 1

Learn how to find the linear equation in slope-intercept form from a table of points. Using the points (1, 4), (2, 3), (3, 2), and (4, 1), discover how to calculate the slope and the y-intercept. Suitable for Grades 7-9.

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