It seems like there is a small error in the equation you provided. The equation -6x + 1 is not a complete linear equation because it lacks the $y$ term. Typically, a linear equation is in the form $y = mx + b$, $ax + by = c$, or a similar complete form.

If the intended equation is simply $y = -6x + 1$, we can proceed from there. If it is something else, please clarify. Assuming it is $y = -6x + 1$, let's find the equation of the line parallel to it and passing through the point $(-3, 3)$.

1. Identify the slope of the given line

The given equation is $y = -6x + 1$, where the slope $m$ is $-6$.

2. Use the slope of the parallel line

Since parallel lines have the same slope, the slope of the new line is also $m = -6$.

3. Use the point-slope form of the equation

The point-slope form is:

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

Substituting the point $(-3, 3)$ and the slope $m = -6$ into this form:

$y - 3 = -6(x + 3)$

4. Simplify to the slope-intercept form

Expand and simplify the equation:

$y - 3 = -6x - 18$

Add 3 to both sides:

$y = -6x - 15$

Final Answer:

The equation of the line parallel to $y = -6x + 1$ and passing through the point $(-3, 3)$ is:

$y = -6x - 15$

Would you like more details on this solution or have any questions?

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Here are some related questions you might find interesting:

1. How do you find the equation of a line that is perpendicular to a given line?
2. What is the geometric meaning of the slope in a linear equation?
3. How can you find the distance between a point and a line?
4. How do you determine if a point lies on a given line?
5. How can you graphically represent a line given its equation?

Tip: When working with parallel lines, always remember they share the same slope, which is key to finding the equation of a line parallel to a given one.