Final answer:
The equation y = x² + 1 is nonproportional because its graph is a parabolic curve, not a straight line, indicating that y does not change proportionally with x.
Step-by-step explanation:
The equation in question, y = x² + 1, is nonproportional. When we talk about proportional relationships, we are referring to scenarios where one variable is directly proportional to another. This means that if one variable changes, the other changes in a consistent manner, which can be represented by a straight line graph passing through the origin. An example of a proportional relationship is y = kx, where k represents the proportionality constant.
In contrast, the equation y = x² + 1 represents a quadratic function. Its graph is a curve called a parabola, not a straight line. Therefore, it does not depict a directly proportional relationship between x and y. The graph of any quadratic function is not a straight line, but a curve that either opens upward or downward. Specifically, if we were to graph the equation y = x² + 1, it would open upward, indicating that as x increases or decreases, y does not change at the same rate. Instead, y increases as the square of x, which is a hallmark of nonproportional relationships.