Final answer:
The equation that represents the relationship shown in the table is y = -3x + 4 (option A).
Step-by-step explanation:
The equation that represents the relationship shown in the table is y = -3x + 4, which is option A.
To determine this, we can plug in the values of x and y from the table into each equation and see which one is consistent with all the values. For example, if we use x = -4, we get y = -3*(-4) + 4 = 12 - 4 = -16, which matches the value in the table. We can do the same for the other values and we will see that only option A, y = -3x + 4, is consistent with all the values in the table.