Final answer:
The equation y = 3x^3 - 3 is nonlinear due to the presence of a cubic term, unlike linear equations which have no exponents higher than one on their x terms and represent straight lines on a graph.
Step-by-step explanation:
The equation in question, y = 3x^3 - 3, is nonlinear because it contains a cubic term (x raised to the third power). For an equation to be considered linear, it must be able to be written in the form y = mx + b, where m represents the slope and b represents the y-intercept. In our given equation, the presence of a cubic term (3x^3) means that the graph of the equation will not be a straight line. Instead, the graph will show a curve that represents a cubic function. This is evident when we compare it to known linear equations, such as y = 6x + 8 or y + 7 = 3x, which have no exponents higher than one on their x terms.
Furthermore, when plotting points and drawing a graph for the given equation as you would for a specific line like y = 9 + 3x, where the slope is consistent, you would see that the values of y for y = 3x^3 - 3 will not form a straight line or have a constant slope.