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The problem asks to find the equation of the line \( y = 3x - 2 \) after it has been translated 3 units to the left.

### Translation of a line:
When a line is translated horizontally, the slope \( m \) remains unchanged. The translation affects only the \( x \)-term in the equation of the line. If we translate the line \( y = mx + b \) horizontally by \( h \) units, the new equation becomes:

\[
y = m(x - h) + b
\]

### In this case:
- The original line is \( y = 3x - 2 \).
- The translation is 3 units to the left, which means \( h = -3 \).

Using the translation formula:

\[
y = 3(x - (-3)) - 2
\]

Simplifying the equation:

\[
y = 3(x + 3) - 2
\]

Thus, the equation of the line after the translation is \( y = 3(x + 3) - 2 \).

### Answer:
The correct option is **C: \( y = 3(x + 3) - 2 \)**.

Let me know if you need further details or clarification!

Here are some additional related questions:
1. How do vertical translations affect the equation of a line?
2. How would the equation change if the line was translated 3 units to the right instead?
3. What is the impact of a vertical translation on the slope?
4. How do you graphically identify the effect of a horizontal translation?
5. Can you describe how translations affect parabolas compared to lines?

**Tip:** When translating graphs, remember that shifting left corresponds to adding to the \( x \)-coordinate, while shifting right corresponds to subtracting.

What is the equation of the line y = 3x - 2 after it has been translated 3 units to the left?

Find out how to translate the line y = 3x - 2 by 3 units to the left. Learn the steps of horizontal translation in linear functions and how the equation changes when the line is shifted. Suitable for Grades 8-10.

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