Final answer:
The rate of change of the equation y = -4x - 7 is -4, which is also known as the slope of the line when graphed.
Step-by-step explanation:
The rate of change of the equation y = -4x - 7 is represented by the coefficient of x, which in this case is -4. This coefficient is also referred to as the slope of the line when graphed on a coordinate plane. Therefore, the correct answer to the student's question would be a) -4. The negative value signifies a downward trend, illustrating how, for each unit increase in x, the corresponding y-value decreases by 4 units. This comprehensive understanding reaffirms the significance of the coefficient as the slope and its role in indicating the direction and steepness of the plotted line.