To determine which of the given sets of points does not represent a linear function, we need to check whether the points in each option have a constant slope. A linear function has a constant slope between any two points.

The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Let's check the slopes for each set of points.

Option A: $(4, -6), (7, -12), (8, -14), (10, -18), (2, -2)$

• Slope between $(4, -6)$ and $(7, -12)$: $\frac{-12 - (-6)}{7 - 4} = \frac{-6}{3} = -2$
• Slope between $(7, -12)$ and $(8, -14)$: $\frac{-14 - (-12)}{8 - 7} = \frac{-2}{1} = -2$
• Slope between $(8, -14)$ and $(10, -18)$: $\frac{-18 - (-14)}{10 - 8} = \frac{-4}{2} = -2$
• Slope between $(10, -18)$ and $(2, -2)$: $\frac{-2 - (-18)}{2 - 10} = \frac{16}{-8} = -2$

Since all the slopes are equal, this represents a linear function.

Option B: $(-2, -6), (1, 0), (4, -30), (0, 2), (7, -96)$

• Slope between $(-2, -6)$ and $(1, 0)$: $\frac{0 - (-6)}{1 - (-2)} = \frac{6}{3} = 2$
• Slope between $(1, 0)$ and $(4, -30)$: $\frac{-30 - 0}{4 - 1} = \frac{-30}{3} = -10$

Since the slopes are not constant, this does not represent a linear function.

Option C: $(-4, 9), (0, 7), (2, 6), (6, 4), (8, 3)$

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

Since all the slopes are equal, this represents a linear function.

Option D: $(2, 18), (6, 50), (-3, -22), (0, 2), (3, 26)$

• Slope between $(2, 18)$ and $(6, 50)$: $\frac{50 - 18}{6 - 2} = \frac{32}{4} = 8$
• Slope between $(6, 50)$ and $(-3, -22)$: $\frac{-22 - 50}{-3 - 6} = \frac{-72}{-9} = 8$
• Slope between $(-3, -22)$ and $(0, 2)$: $\frac{2 - (-22)}{0 - (-3)} = \frac{24}{3} = 8$
• Slope between $(0, 2)$ and $(3, 26)$: $\frac{26 - 2}{3 - 0} = \frac{24}{3} = 8$

Since all the slopes are equal, this represents a linear function.

Conclusion:

The set of points in Option B does not represent a linear function.

Would you like a further breakdown of the solution?

Here are 5 related questions:

1. What defines a linear function in terms of slope?
2. How can we graphically interpret non-linear functions?
3. Can a set of points represent a non-linear function but still have some constant slopes?
4. How do we compute the slope if one or both points have negative coordinates?
5. What role does the slope play in determining the behavior of a function?

Tip: To check if a function is linear, ensure that the rate of change (slope) between all consecutive points remains constant.