The equation of a line parallel to another line will have the same slope. The given line is $y = -3x + 2$, where the slope is $-3$.

For a line parallel to this, we use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope of the line (in this case, $-3$)
• $(x_1, y_1)$ is the point the line passes through (in this case, $(3, 2)$)

Substituting the values:

$y - 2 = -3(x - 3)$

Now, simplify the equation:

$y - 2 = -3x + 9$

$y = -3x + 11$

So, the equation of the line is:

$y = -3x + 11$

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. How do you find the equation of a line perpendicular to $y = -3x + 2$?
2. What is the general form of a line's equation?
3. How would the equation change if the line passed through another point?
4. Can you write the equation of a line parallel to $y = 4x - 7$?
5. What is the significance of the slope in parallel lines?

Tip: Parallel lines always have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.