The question asks which of the given equations represents a linear function. Let's analyze each option:

A: $y = 2^x$

This equation represents an exponential function, not a linear function. Linear functions have the general form $y = mx + b$.

B: $-x^3 + y = 2$

Rearranging gives $y = x^3 + 2$. The $x^3$ term makes this a cubic function, not linear.

C: $y = \sqrt{x - 3}$

This equation involves a square root, so it is not linear.

D: $3|x| - 3y = 18$

Rewriting as $3y = 3|x| - 18$, then dividing by 3, we have $y = |x| - 6$. The absolute value function $|x|$ is not linear.

E: $3x - 2y = -8$

Rearranging gives $y = \frac{3}{2}x + 4$. This is a linear function since it matches the general form $y = mx + b$.

Correct Answer: E

Let me know if you'd like further clarification!

Here are 5 questions to explore further:

1. What are the key features of a linear function?
2. How do you distinguish exponential functions from linear ones?
3. Can a cubic or quadratic function ever appear "linear" in small intervals?
4. Why does the absolute value function $|x|$ fail the criteria for linearity?
5. How do changes in $m$ and $b$ in $y = mx + b$ affect the graph of a linear function?

Tip: A quick test for linearity is checking if the equation forms a straight line when plotted on a graph!