Question

1. a cell phone company charges a flat fee of $40.00 per month and an additional $20.00 per month for each phone on the plan.

a. is the relationship between the total monthly cost and the number of phones on the plan a proportional relationship? explain your thinking.
b. justify your thinking by creating a table or a graph.
for problems 2 and 3, identify whether the relationship is proportional. if so, define your variables and write an equation. if not, change a value to make it a proportional relationship.

1. each day of doggie daycare costs $25.

Explanation:

Step1: Recall proportional - relationship definition

A proportional relationship is of the form $y = kx$ where $k$ is a constant of proportionality and when $x = 0$, $y=0$. Let $x$ be the number of phones and $y$ be the total monthly cost. The cost function is $y=20x + 40$. When $x = 0$, $y = 40
eq0$. So, it is not a proportional relationship.

Step2: Create a table for part b

Number of Phones ($x$)	Total Monthly Cost ($y$)
1	$20\times1 + 40=60$
2	$20\times2+40 = 80$
3	$20\times3 + 40=100$

For problem 2:
Let $x$ be the number of days of dog - gie daycare and $y$ be the total cost. The relationship is $y = 25x$. Since it is in the form $y=kx$ (where $k = 25$) and when $x = 0$, $y = 0$, it is a proportional relationship.

Answer:

a. No. The relationship between the total monthly cost $y$ and the number of phones $x$ is $y = 20x+40$. In a proportional relationship $y=kx$ and when $x = 0$, $y$ should be $0$, but here when $x = 0$, $y = 40$.
b. See the table above.

1. Yes. Let $x$ be the number of days of dog - gie daycare and $y$ be the total cost. The equation is $y = 25x$.