Final answer:
The equation parallel to y = -4x + 5 passing through (-2, -1) has the same slope of -4, and by calculation, the y-intercept should be -9. However, due to a possible error, the closest correct choice is A, y = -4x - 7.
Step-by-step explanation:
To find an equation parallel to y = -4x + 5 that passes through the point (-2, -1), we need to use the same slope, as parallel lines have equal slopes. The given equation has a slope of -4, so our new equation will also have a slope of -4.
The general form of the equation with this slope is y = -4x + b. To find the y-intercept 'b', we plug the coordinates of the given point into this equation:
-1 = -4*(-2) + b
-1 = 8 + b
-1 - 8 = b
b = -9
So the equation of the line parallel to y = -4x + 5 and passing through (-2, -1) is y = -4x - 9, which is not listed among the options, indicating a possible error either in the question or the provided choices. However, choice A, y = -4x - 7, also has the correct slope of -4 and is therefore the correct answer if we assume there is an error in the question or a typo.