Final answer:
The equation of the line parallel to y = -3x + 1 that passes through (-4, -6) is y = -3x - 18, obtained by keeping the same slope and solving for the y-intercept using the given point.
Step-by-step explanation:
To find the equation of a line that is parallel to y = -3x + 1, we need to use the same slope. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since the given line has a slope of -3, the parallel line will also have a slope of -3.
Now, we can use the point (-4, -6) to find the y-intercept. Substitute the values of x = -4 and y = -6 into the equation y = mx + b to solve for b: -6 = -3*(-4) + b. Simplifying the equation, we have -6 = 12 + b, or b = -18.
Therefore, the equation of the line parallel to y = -3x + 1 that passes through (-4, -6) is y = -3x - 18.