To write the linear equation for the given table, we first observe that as $x$ increases by 1, $y$ also increases by 1. This indicates a slope ($m$) of 1.

Next, we calculate the y-intercept ($b$) by substituting one of the points into the equation $y = mx + b$. Using the point $(2, 1)$:

$1 = 1(2) + b$

$1 = 2 + b$

$b = -1$

Thus, the linear equation is:

$y = x - 1$

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Would you like additional explanations or have further questions?
Here are 5 related questions for deeper understanding:

1. How do you determine the slope of a linear equation from a table?
2. What happens to the equation if the y-values change by a different constant rate?
3. Can you write a linear equation for a table where the x-values decrease?
4. How can you graph this equation using the slope and y-intercept?
5. What is the significance of the y-intercept in real-world problems?

Tip: When working with a table, always verify if the relationship is linear by checking if the differences in $y$ values are consistent with changes in $x$.