Final answer:
The linear function representing Sung-Hi filling a sandbox with sand must have an initial value of 0 pounds, assuming the sandbox starts empty, and a rate of change of 20 pounds per minute if she adds sand at a consistent rate.
Thus, the correct option is A.
Step-by-step explanation:
The situation described involving Sung-Hi filling a sandbox with sand suggests a linear relationship between the amount of sand in the sandbox and time.
Since the rate at which the sandbox is filled is constant, this indicates that there is a steady rate of change in the amount of sand added per unit of time. To determine which statement must be true regarding the linear function that represents this situation, it is important to understand what the initial value and rate of change mean in this context.
The initial value in a linear equation of the form y = mx + b would represent the starting quantity of sand in the sandbox, which would logically be 0 pounds if starting from empty.
The rate of change, represented by 'm' in the linear equation, will signify how quickly sand is being added to the sandbox per minute.
Therefore, answer (a) The initial value must be 0 pounds is correct, assuming the sandbox starts empty, and (d) The rate of change must be 20 pounds per minute is correct if Sung-Hi consistently adds 20 pounds of sand each minute.