To determine which set of ordered pairs represents a linear function, we need to check whether the relationship between the $x$-values and $y$-values follows a straight line. For this, the slope between any two points should be constant.

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let’s check each set of ordered pairs:

Set A: $\{(0, -3), (1, -1), (2, 1), (3, 4)\}$

1. Slope between $(0, -3)$ and $(1, -1)$: $m = \frac{-1 - (-3)}{1 - 0} = \frac{2}{1} = 2$
2. Slope between $(1, -1)$ and $(2, 1)$: $m = \frac{1 - (-1)}{2 - 1} = \frac{2}{1} = 2$
3. Slope between $(2, 1)$ and $(3, 4)$: $m = \frac{4 - 1}{3 - 2} = \frac{3}{1} = 3$

Since the slopes are not consistent (2 and 3), Set A does not represent a linear function.

Set B: $\{(-7, -3), (-1, 0), (4, 3), (9, 6)\}$

1. Slope between $(-7, -3)$ and $(-1, 0)$: $m = \frac{0 - (-3)}{-1 - (-7)} = \frac{3}{6} = \frac{1}{2}$
2. Slope between $(-1, 0)$ and $(4, 3)$: $m = \frac{3 - 0}{4 - (-1)} = \frac{3}{5}$
3. Slope between $(4, 3)$ and $(9, 6)$: $m = \frac{6 - 3}{9 - 4} = \frac{3}{5}$

Since the slopes are not consistent ( $\frac{1}{2}$ and $\frac{3}{5}$), Set B does not represent a linear function.

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

1. Slope between $(0, 9)$ and $(3, 4)$: $m = \frac{4 - 9}{3 - 0} = \frac{-5}{3}$
2. Slope between $(3, 4)$ and $(6, -2)$: $m = \frac{-2 - 4}{6 - 3} = \frac{-6}{3} = -2$
3. Slope between $(6, -2)$ and $(9, -8)$: $m = \frac{-8 - (-2)}{9 - 6} = \frac{-6}{3} = -2$

Since the slopes between the last two points are the same, but not consistent with the first pair ($\frac{-5}{3}$), Set C does not represent a linear function.

Set D: $\{(-2, -8), (1, -7), (4, -6), (7, -5)\}$

1. Slope between $(-2, -8)$ and $(1, -7)$: $m = \frac{-7 - (-8)}{1 - (-2)} = \frac{1}{3}$
2. Slope between $(1, -7)$ and $(4, -6)$: $m = \frac{-6 - (-7)}{4 - 1} = \frac{1}{3}$
3. Slope between $(4, -6)$ and $(7, -5)$: $m = \frac{-5 - (-6)}{7 - 4} = \frac{1}{3}$

Since the slopes are consistent ($\frac{1}{3}$ for each pair), Set D represents a linear function.

Conclusion:

The set of ordered pairs that represents a linear function is Set D.

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Would you like further explanations or details on any of the calculations? Here are 5 questions that might help you dive deeper:

1. How can we determine if a set of ordered pairs is a function?
2. What does it mean for a function to be linear?
3. How can we calculate the slope between two points?
4. What are some graphical ways to determine if a relation is linear?
5. How does the consistency of the slope relate to the definition of a straight line?

Tip: Always check the slope between multiple pairs of points to verify if a set of points forms a straight line.