Final answer:
The equation of a line that is parallel to a given line with the same slope can be found by using the point-slope form. The correct equation for a line parallel to the given line and passing through the point (-4, -6) is y = -6.
Step-by-step explanation:
The equation of a line that is parallel to a given line can be found using the same slope as the given line. Since parallel lines have the same slope, we can use the slope of the given line to find the equation of the parallel line.
Let's assume the equation of the given line is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel, the slope of the parallel line will also be m.
So, to find the equation of the parallel line that passes through the point (-4, -6), we can substitute the slope of the given line into the point-slope form of the equation: y - y1 = m(x - x1).
Therefore, the equation of the line that is parallel to the given line and passes through the point (-4, -6) is: y - (-6) = mx - (-4).
The correct answer is: c) y = -6.