To determine which point does not lie on the line $y = 3x - 2$, we substitute the $x$- and $y$-values of each point into the equation and check if the equation holds true.

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Testing each point:

1. Point A: $(0, -2)$
   Substituting $x = 0$ into $y = 3x - 2$:
   $y = 3(0) - 2 = -2$
   The $y$-value matches ($y = -2$), so $(0, -2)$ lies on the line.

2. Point B: $(1, 1)$
   Substituting $x = 1$ into $y = 3x - 2$:
   $y = 3(1) - 2 = 1$
   The $y$-value matches ($y = 1$), so $(1, 1)$ lies on the line.

3. Point C: $(-1, 5)$
   Substituting $x = -1$ into $y = 3x - 2$:
   $y = 3(-1) - 2 = -3 - 2 = -5$
   The $y$-value does not match ($y = 5$), so $(-1, 5)$ does not lie on the line.

4. Point D: $(2, 4)$
   Substituting $x = 2$ into $y = 3x - 2$:
   $y = 3(2) - 2 = 6 - 2 = 4$
   The $y$-value matches ($y = 4$), so $(2, 4)$ lies on the line.

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Conclusion:

The point that does not lie on the line is C: $(-1, 5)$.

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Do you want further details or have any questions?

Here are 5 related questions to explore further:

1. How do you derive the equation of a line from two given points?
2. What is the slope-intercept form of a linear equation, and what do its components represent?
3. How can you determine if a point lies on a line without graphing?
4. What is the geometric interpretation of a point not lying on a line?
5. How do you find the distance from a point to a line?

Tip: To confirm points on a line quickly, always check the equation by substitution and verify both sides match.