1. **Problem Statement:** Given points $(-3, -5)$, $(-1, -6)$, and $(5, -7)$, determine the type of sequence or function they represent and find an explicit formula matching the graph. 2. **Identify the type of function:** The points lie on a straight line, indicating a linear function. This is because the change in $y$ relative to $x$ is constant. 3. **Formula for a linear function:** The general form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - (-5)}{-1 - (-3)} = \frac{-6 + 5}{-1 + 3} = \frac{-1}{2} = -\frac{1}{2}$$ 5. **Find the y-intercept $b$:** Use point $(-3, -5)$: $$-5 = -\frac{1}{2} \times (-3) + b \implies -5 = \frac{3}{2} + b \implies b = -5 - \frac{3}{2} = -\frac{10}{2} - \frac{3}{2} = -\frac{13}{2}$$ 6. **Explicit formula:** $$y = -\frac{1}{2}x - \frac{13}{2}$$ 7. **Interpretation:** The function is linear, not arithmetic or geometric sequences or exponential. **Final answer:** The graph represents a linear function with formula $$y = -\frac{1}{2}x - \frac{13}{2}$$.