1. **State the problem:** We are given two points on a graph: (2, 2) and (6, -1). We need to find the explicit formula of the linear function that passes through these points. 2. **Recall the formula for a linear function:** The general form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using the points (2, 2) and (6, -1), we get: $$m = \frac{-1 - 2}{6 - 2} = \frac{-3}{4} = -\frac{3}{4}$$ 4. **Find the y-intercept $b$:** Substitute one point and the slope into the equation $y = mx + b$ to solve for $b$. Using point (2, 2): $$2 = -\frac{3}{4} \times 2 + b$$ $$2 = -\frac{3}{2} + b$$ Add $\frac{3}{2}$ to both sides: $$b = 2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2}$$ 5. **Write the explicit formula:** $$y = -\frac{3}{4}x + \frac{7}{2}$$ 6. **Interpretation:** This formula represents a line with a negative slope, matching the graph where $y$ decreases as $x$ increases. **Final answer:** $$y = -\frac{3}{4}x + \frac{7}{2}$$