1. **State the problem:** We need to find the linear equation $y = mx + b$ that fits the given table of values: $$\begin{array}{c|c} x & y \\ \hline 2 & 0 \\ 3 & 1 \\ 4 & 2 \\ 5 & 3 \end{array}$$ 2. **Find the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(2,0)$ and $(3,1)$: $$m = \frac{1 - 0}{3 - 2} = \frac{1}{1} = 1$$ 3. **Write the equation with slope:** $$y = 1 \cdot x + b = x + b$$ 4. **Find the y-intercept $b$:** Substitute one point, for example $(2,0)$: $$0 = 1 \cdot 2 + b$$ $$0 = 2 + b$$ $$b = -2$$ 5. **Final equation:** $$y = x - 2$$ This equation matches all points in the table.