Final answer:
The slope of the given line 4x - y = 7 is 4. Because parallel lines have the same slope, the line through the point (0, -4) will have a slope of 4 and y-intercept -4, resulting in the equation y = 4x - 4.
Step-by-step explanation:
To find an equation of a line that is parallel to another and passes through a given point, we first need to determine the slope of the given line. Looking at the equation 4x - y = 7, we can rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. In doing so, the equation becomes y = 4x - 7. Hence, the slope of the given line is 4. Since parallel lines have the same slope, the slope of our new line will also be 4.
The line we are looking for passes through the point (0, -4), which means that the y-intercept is -4. By plugging the slope and y-intercept into the slope-intercept form of a line, we get y = 4x - 4. Therefore, the correct equation of the line we are seeking is y = 4x - 4, which corresponds to option D.