To solve this problem, we need to find the linear equation that fits the data points in the table. The equation will be in the slope-intercept form, $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept.

Step 1: Identify two points from the table.

The table gives the following points:

• (2, 1)
• (3, 2)
• (4, 3)
• (5, 4)

Step 2: Calculate the slope $m$.

The slope is calculated as:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

Let's use the points (2, 1) and (3, 2):

$m = \frac{{2 - 1}}{{3 - 2}} = \frac{1}{1} = 1$

So, the slope $m = 1$.

Step 3: Find the y-intercept $b$.

Now that we know $m = 1$, we can use one of the points to find the y-intercept. Let's use the point (2, 1) and substitute into the equation $y = mx + b$:

$1 = 1(2) + b$

Solving for $b$:

$1 = 2 + b \quad \Rightarrow \quad b = 1 - 2 = -1$

Step 4: Write the equation.

Now that we have $m = 1$ and $b = -1$, the equation is:

$y = x - 1$

This is the linear equation that fits the data from the table.

Do you want more details or have any questions?

Here are five related questions to explore:

1. How would you find the equation if the points in the table had a negative slope?
2. What happens to the equation if you change the y-intercept?
3. How can you verify that a given equation fits all the points in a table?
4. How does the slope influence the steepness of a line?
5. What would be the equation if the slope was zero?

Tip: Always double-check your slope calculation by using multiple points to ensure consistency.