Final answer:
The equation of the line parallel to y = -4x + 3 and passing through the point (-5, -7) is y = -4x - 27, which corresponds to answer choice (a).
Step-by-step explanation:
The student is asking to write the equation of a line in slope-intercept form that is parallel to a given line and passes through a specific point. The given line has the equation y = -4x + 3. Parallel lines have the same slope, so the new line will have a slope of -4 as well. To find the y-intercept (b), we use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept, and the point (-5, -7) through which the line passes.
Substitute the values into the equation:
-7 = (-4)(-5) + b
-7 = 20 + b
b = -7 - 20
b = -27
Therefore, the equation of the line is y = -4x - 27, corresponding to answer choice (a).