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 has the form $y = kx$, where $k$ is a constant of proportionality and passes through the origin $(0,0)$. Let $x$ be the number of phones and $y$ be the total monthly cost. The cost function is $y=20x + 40$.

Step2: Check if it passes through the origin

When $x = 0$, $y=20\times0 + 40=40$. Since it does not pass through the origin $(0,0)$, the relationship is not proportional.

Step3: 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 the dog - gie daycare problem:
Let $x$ be the number of days and $y$ be the total cost. The cost function is $y = 25x$.

Step4: Check proportionality

This relationship is of the form $y=kx$ (where $k = 25$) and when $x = 0$, $y=0$. So it is a proportional relationship.

Answer:

a. No. The relationship is $y = 20x+40$ and does not pass through the origin $(0,0)$.
b. See the table above.

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