Question

Peter enters a hot dog eating contest. Peter's friend calculates that on average, Peter eats 2 hot dogs per minute. They write the equation y = 2x in order to predict how many hot dogs Peter can eat in a 30-minute contest, where x stands for the amount of time in minutes and y stands for the total number of hot dogs.

A) Does the equation represent a proportional relationship? Explain your reasoning.

B) What is the unit rate of change for this situation?

Answer 1

A) The equation y = 2x represents a proportional relationship. This is because the values of y are directly proportional to the values of x. In other words, as x increases, y also increases by the same factor. This is the definition of a proportional relationship.

B) The unit rate of change for this situation is 2 hot dogs per minute. This is because the equation y = 2x represents a linear relationship, where the rate of change (the slope) is constant. The unit rate of change is the slope of the line, which in this case is 2. This means that for every 1 minute that passes, Peter eats 2 hot dogs.