1. **Problem Statement:** We are given a table of values for variables $x$ and $y$ and need to find the linear equation that relates them. 2. **Formula Used:** The general form of a linear equation is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Finding the Slope $m$:** The slope is calculated by the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points from the table. 4. **Calculate $m$ using two points:** Suppose the table gives points $(x_1, y_1)$ and $(x_2, y_2)$. 5. **Find $b$ (y-intercept):** Substitute one point and the slope into the equation $$y = mx + b$$ and solve for $b$. 6. **Write the final equation:** Substitute $m$ and $b$ back into $$y = mx + b$$. 7. **Example:** If the table has points $(1, 3)$ and $(3, 7)$: $$m = \frac{7 - 3}{3 - 1} = \frac{4}{2} = 2$$ Substitute $(1, 3)$: $$3 = 2 \times 1 + b \Rightarrow b = 3 - 2 = 1$$ Final equation: $$y = 2x + 1$$