1. **State the problem:** We are given three points: (1, -6), (5, -7), and (9, -8). We need to determine which type of function or sequence these points represent and find an explicit formula that matches the graph. 2. **Identify the type of sequence or function:** The options are arithmetic sequence, geometric sequence, linear function, or exponential function. 3. **Check if the points form an arithmetic sequence:** An arithmetic sequence has a constant difference between consecutive terms. Calculate the differences in y-values: $$-7 - (-6) = -1$$ $$-8 - (-7) = -1$$ The differences are constant (-1), so the y-values form an arithmetic sequence. 4. **Check if the points form a geometric sequence:** A geometric sequence has a constant ratio between consecutive terms. Calculate the ratios: $$\frac{-7}{-6} \approx 1.1667$$ $$\frac{-8}{-7} \approx 1.1429$$ The ratios are not constant, so it is not a geometric sequence. 5. **Check if the points form a linear function:** A linear function has the form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. Calculate the slope $$m$$ using two points, for example (1, -6) and (5, -7): $$m = \frac{-7 - (-6)}{5 - 1} = \frac{-1}{4} = -\frac{1}{4}$$ Use point-slope form to find $$b$$: $$y = mx + b \Rightarrow -6 = -\frac{1}{4} \times 1 + b \Rightarrow b = -6 + \frac{1}{4} = -\frac{23}{4}$$ So the explicit formula is: $$y = -\frac{1}{4}x - \frac{23}{4}$$ 6. **Check if the points form an exponential function:** An exponential function has the form $$y = ab^x$$. Since the differences in y-values are constant and the ratios are not, it is unlikely to be exponential. **Conclusion:** The graph represents a linear function. **Final explicit formula:** $$y = -\frac{1}{4}x - \frac{23}{4}$$