1. **State the problem:** Find the equation of the function $f(x)$ that passes through the points $(-6, -6)$, $(-2, -7)$, and $(2, -8)$. 2. **Identify the type of function:** Since the points appear to lie on a straight line, we assume $f(x)$ is linear, so $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Use the formula for slope between two points $(x_1, y_1)$ and $(x_2, y_2)$: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(-6, -6)$ and $(-2, -7)$: $$m = \frac{-7 - (-6)}{-2 - (-6)} = \frac{-7 + 6}{-2 + 6} = \frac{-1}{4} = -\frac{1}{4}$$ 4. **Verify slope with another pair:** Using $(-2, -7)$ and $(2, -8)$: $$m = \frac{-8 - (-7)}{2 - (-2)} = \frac{-8 + 7}{2 + 2} = \frac{-1}{4} = -\frac{1}{4}$$ The slope is consistent, confirming a linear function. 5. **Find the y-intercept $b$:** Use point-slope form with one point, for example $(-6, -6)$: $$y = mx + b \Rightarrow -6 = -\frac{1}{4} \times (-6) + b$$ $$-6 = \frac{6}{4} + b \Rightarrow b = -6 - \frac{3}{2} = -6 - 1.5 = -7.5$$ 6. **Write the function:** $$f(x) = -\frac{1}{4}x - 7.5$$ This is the equation of the line passing through the given points. **Final answer:** $$f(x) = -\frac{1}{4}x - 7.5$$