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To determine which of the given equations has a line with a slope of 3, we can recall the slope-intercept form of a linear equation:

\[
y = mx + b
\]

In this equation, \( m \) represents the slope, and \( b \) is the y-intercept.

Let's check the slope \( m \) for each option:

- **A) \( y = \frac{1}{3}x \)**: The slope here is \( \frac{1}{3} \), not 3.
- **B) \( y = x - 3 \)**: The slope here is \( 1 \), not 3.
- **C) \( y = 3x + 2 \)**: The slope here is \( 3 \), which matches the required slope.
- **D) \( y = 6x + 3 \)**: The slope here is \( 6 \), not 3.

Thus, the correct answer is **C) \( y = 3x + 2 \)**.

Would you like more details or explanations? 

Here are 5 related questions you can explore:
1. How can you determine the y-intercept from a linear equation?
2. What happens if the slope is negative?
3. Can a vertical line have a slope?
4. How does changing the slope affect the steepness of the line?
5. What does a slope of zero mean for the line's direction?

**Tip:** The larger the slope, the steeper the line will be on the graph!

In the xy-plane, the graph of which of the following equations is a line with a slope of 3?

Understand how to determine the slope of a line in a linear equation. This example asks you to identify which equation has a slope of 3. Learn key concepts in linear equations and slope-intercept form, ideal for Grades 8-10.

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