The slope of a line parallel to the line $y = 3x + 2$ is the same as the slope of the given line. The equation is in slope-intercept form, $y = mx + b$, where $m$ represents the slope. For the line $y = 3x + 2$, the slope $m$ is $3$.

Thus, the slope of a line parallel to this line is also $3$.

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Here are 5 related questions:

1. What is the slope of a line perpendicular to $y = 3x + 2$?
2. How do you find the equation of a line given a point and the slope?
3. What is the y-intercept of the line $y = 3x + 2$?
4. How can you determine if two lines are parallel from their equations?
5. What is the equation of a line parallel to $y = 3x + 2$ and passing through the point $(1, 4)$?

Tip: Parallel lines have identical slopes, while perpendicular lines have slopes that are negative reciprocals of each other.