Question

The following table represents the total cost, in dollars (y) to join a gym for x number of months. The cost includes a one-time joining fee of $10. Does the data in the table represent a proportional relationship or a non-proportional relationship? How do you know?

x 1 2 3 4 5
y 25 40 55 70 85


Attachment is for the second question.

The graph below shows the average daily temperature over the period of a year. Explain how each labeled section of the graph relates to the four seasons.

Answer 1

Not proportional.

A winter, B is spring, C is summer and D is fall.

Explanation:

A proportional relationship has a constant of proportional which can be formed by a ratio between any y and x values of the function. The constant will be the same every time.

The ratio y/x is 25/1, 40/2, 55/3, 70/4, and 85/5. These simplify to 25, 20, 13.33, etc. These are not the same values. This is not proportional.

In the attached graph the lows or "valleys" are the coldest parts of the year. A and D are likely Fall and Winter. While B grows and temperatures get higher then B is likely Spring. This means C is summer since it has the highest temperatures.