1. The problem asks which set of ordered pairs $(x, y)$ could represent a linear function. 2. A linear function has a constant slope between any two points. The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. We will calculate the slope between consecutive points in each set and check if the slope is constant. 4. For set A: $\{(-4, 8), (-1, 7), (2, 5), (5, 4)\}$ - Slope between $(-4,8)$ and $(-1,7)$: $$m = \frac{7 - 8}{-1 - (-4)} = \frac{-1}{3} = -\frac{1}{3}$$ - Slope between $(-1,7)$ and $(2,5)$: $$m = \frac{5 - 7}{2 - (-1)} = \frac{-2}{3} = -\frac{2}{3}$$ - Slope between $(2,5)$ and $(5,4)$: $$m = \frac{4 - 5}{5 - 2} = \frac{-1}{3} = -\frac{1}{3}$$ Slopes are $-\frac{1}{3}, -\frac{2}{3}, -\frac{1}{3}$, not constant, so A is not linear. 5. For set B: $\{(-6, 9), (-2, 3), (0, 0), (2, -3)\}$ - Slope between $(-6,9)$ and $(-2,3)$: $$m = \frac{3 - 9}{-2 - (-6)} = \frac{-6}{4} = -\frac{3}{2}$$ - Slope between $(-2,3)$ and $(0,0)$: $$m = \frac{0 - 3}{0 - (-2)} = \frac{-3}{2} = -\frac{3}{2}$$ - Slope between $(0,0)$ and $(2,-3)$: $$m = \frac{-3 - 0}{2 - 0} = \frac{-3}{2} = -\frac{3}{2}$$ Slopes are all $-\frac{3}{2}$, constant, so B is linear. 6. For completeness, sets C and D can be checked but since only the first question is solved, we conclude: **Answer:** Set B could represent a linear function because it has a constant slope between all consecutive points.