Question

"The admission for the chess team to go to the waterpark can be represented by the equation y = 12x, where y is the total cost of admission for x students. Determine whether the function is proportional or non-proportional. Explain."

Answer 1

The equation y = 12x represents a proportional relationship with a constant of proportionality of 12, indicating that the total cost increases at a constant rate per student with no fixed cost.

Step-by-step explanation:

The function described by the equation y = 12x for the chess team's admission cost to a waterpark is a proportional relationship, since the ratio of total cost to the number of students remains constant. This means for every additional student, the total cost increases at a constant rate of 12. There is no starting fee or fixed cost. A proportional function can be identified by its having a graph that is a straight line passing through the origin (0,0) and it can be represented mathematically in the form of y = mx where m is the constant of proportionality. In this case, the slope or the constant of proportionality is 12, which represents the cost per student for admission.