1. **State the problem:** We need to find the linear equation in slope-intercept form $y = mx + b$ that fits the given table of points: $(4, 28)$, $(5, 29)$, $(6, 30)$, and $(7, 31)$. 2. **Recall the formula:** The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope is the change in $y$ divided by the change in $x$ between any two points. $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(4, 28)$ and $(5, 29)$: $$m = \frac{29 - 28}{5 - 4} = \frac{1}{1} = 1$$ 4. **Find the y-intercept $b$:** Use the slope and one point to solve for $b$. Using point $(4, 28)$: $$28 = 1 \times 4 + b$$ $$b = 28 - 4 = 24$$ 5. **Write the equation:** Substitute $m = 1$ and $b = 24$ into the slope-intercept form. $$y = 1x + 24$$ or simply $$y = x + 24$$ This equation matches all points in the table, confirming it is correct.