https://file.aiquickdraw.com/mathbot/file/1726076698860e10vpplh.jpg

Let's analyze the table of values provided:

| x | y |
|---|---|
| 2 | 0 |
| 3 | 1 |
| 4 | 2 |
| 5 | 3 |

The goal is to write a linear equation of the form:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Calculate the slope (\( m \))
To find the slope, we use the formula:

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

Taking two points from the table, say \( (x_1, y_1) = (2, 0) \) and \( (x_2, y_2) = (3, 1) \):

\[
m = \frac{1 - 0}{3 - 2} = \frac{1}{1} = 1
\]

So, the slope \( m = 1 \).

### Step 2: Determine the y-intercept (\( b \))
We use one of the points from the table and substitute into the equation \( y = mx + b \).

Using \( (2, 0) \):

\[
0 = 1(2) + b
\]

Solving for \( b \):

\[
0 = 2 + b \quad \Rightarrow \quad b = -2
\]

### Step 3: Write the equation
Thus, the linear equation is:

\[
y = x - 2
\]

This is the equation that describes the relationship between \( x \) and \( y \) in the given table.

Would you like further details or have any questions? Here are 5 related questions to explore:

1. How can we verify the correctness of the equation with other points in the table?
2. What happens to the equation if the slope were different?
3. How does the y-intercept affect the graph of the linear equation?
4. What is the general approach to find the equation from any given table of values?
5. How does this equation relate to the graphical representation of a line?

**Tip**: Always use at least two points from the table to calculate the slope for accuracy!

Write the linear equation that gives the rule for this table. Write your answer as an equation with y first, followed by an equals sign.

Learn how to determine the linear equation y = x - 2 from a table of x and y values (x: 2, 3, 4, 5 and y: 0, 1, 2, 3). This solution includes finding the slope and y-intercept. Suitable for students in Grades 6-8.

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