To determine which set of ordered pairs could represent a linear function, we need to check if the slope between each pair of points is consistent.

The slope between any two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated as:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Let's calculate the slope for each set of ordered pairs:

Set A: $\{(0, -8), (3, -5), (6, -2), (9, 1)\}$

1. Between $(0, -8)$ and $(3, -5)$: $\frac{-5 - (-8)}{3 - 0} = \frac{3}{3} = 1$
2. Between $(3, -5)$ and $(6, -2)$: $\frac{-2 - (-5)}{6 - 3} = \frac{3}{3} = 1$
3. Between $(6, -2)$ and $(9, 1)$: $\frac{1 - (-2)}{9 - 6} = \frac{3}{3} = 1$

All slopes are equal, so Set A represents a linear function.

Set B: $\{(3, 2), (4, 0), (7, -6), (8, -9)\}$

1. Between $(3, 2)$ and $(4, 0)$: $\frac{0 - 2}{4 - 3} = \frac{-2}{1} = -2$
2. Between $(4, 0)$ and $(7, -6)$: $\frac{-6 - 0}{7 - 4} = \frac{-6}{3} = -2$
3. Between $(7, -6)$ and $(8, -9)$: $\frac{-9 - (-6)}{8 - 7} = \frac{-3}{1} = -3$

The slope is not consistent, so Set B does not represent a linear function.

Set C: $\{(-9, 7), (-3, 3), (3, -1), (9, -4)\}$

1. Between $(-9, 7)$ and $(-3, 3)$: $\frac{3 - 7}{-3 - (-9)} = \frac{-4}{6} = -\frac{2}{3}$
2. Between $(-3, 3)$ and $(3, -1)$: $\frac{-1 - 3}{3 - (-3)} = \frac{-4}{6} = -\frac{2}{3}$
3. Between $(3, -1)$ and $(9, -4)$: $\frac{-4 - (-1)}{9 - 3} = \frac{-3}{6} = -\frac{1}{2}$

The slope is not consistent, so Set C does not represent a linear function.

Set D: $\{(-4, 4), (-1, 0), (2, -5), (5, -9)\}$

1. Between $(-4, 4)$ and $(-1, 0)$: $\frac{0 - 4}{-1 - (-4)} = \frac{-4}{3} = -\frac{4}{3}$
2. Between $(-1, 0)$ and $(2, -5)$: $\frac{-5 - 0}{2 - (-1)} = \frac{-5}{3} = -\frac{5}{3}$
3. Between $(2, -5)$ and $(5, -9)$: $\frac{-9 - (-5)}{5 - 2} = \frac{-4}{3} = -\frac{4}{3}$

The slope is not consistent, so Set D does not represent a linear function.

Conclusion:

Only Set A represents a linear function because the slope between all pairs of points is consistent.

Would you like more details or have any other questions?

Here are five related questions to consider:

1. How can you identify a non-linear function from a set of points?
2. What is the equation of the line represented by Set A?
3. How do you calculate the y-intercept of a line from its slope and a point?
4. Can a function be linear if its slope is zero?
5. How do parallel lines relate to their slopes?

Tip: When verifying linearity in a function, check if the difference in y-values over the difference in x-values is constant across all pairs of points.