1. **Problem Statement:** We are given two points from a graph: (2, 2) and (6, -1). We need to determine which type of sequence or function the graph represents and find an explicit formula that matches it. 2. **Types of sequences/functions:** - An arithmetic sequence has a constant difference between terms. - A geometric sequence has a constant ratio between terms. - A linear function has the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. - An exponential function has the form $y = ab^x$, where $a$ is the initial value and $b$ is the base. 3. **Check if the points fit a linear function:** Calculate the slope $m$ using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 2}{6 - 2} = \frac{-3}{4} = -0.75$$ 4. **Find the y-intercept $b$:** Use one point, for example (2, 2), and the slope $m = -0.75$: $$2 = -0.75 \times 2 + b \implies 2 = -1.5 + b \implies b = 3.5$$ 5. **Write the explicit linear function:** $$y = -0.75x + 3.5$$ 6. **Interpretation:** The points decrease linearly, which matches the slope and intercept found. This confirms the graph represents a linear function. **Final answer:** The graph represents a linear function with explicit formula $$y = -0.75x + 3.5$$.