Question

1. maya and her friends are each saving money to buy a new video game. the relationship between the number of weeks and the amount saved is represented for maya and each friend.

maya		victor		allie
1	$122
5	$210
6	$232			y = 22x

which statement is true about the relationships represented?
a. both allie and maya are saving money at the same rate.
b. allie started with an initial amount of money already saved at 0 weeks.
c. both maya and victor are saving money at the same rate.
d. allie and mayas savings are represented by proportional relationships.

Explanation:

Step1: Find Maya's saving - rate

The rate of change (saving - rate) for Maya can be found using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,122)$ and $(x_2,y_2)=(5,210)$. Then $m_{Maya}=\frac{210 - 122}{5 - 1}=\frac{88}{4}=22$.

Step2: Analyze Allie's saving - rate

Allie's relationship is given by $y = 22x$, and the coefficient of $x$ is the rate of change. So $m_{Allie}=22$.

Step3: Analyze Victor's saving - rate

For Victor, we need to find two points on the line. Let's assume the line passes through $(0, 50)$ and $(8,210)$ (estimated from the graph). Then $m_{Victor}=\frac{210 - 50}{8 - 0}=\frac{160}{8}=20$.

Step4: Evaluate each option

• Option A: Since $m_{Maya}=22$ and $m_{Allie}=22$, both Allie and Maya are saving money at the same rate.
• Option B: For Allie, when $x = 0$, $y=22\times0 = 0$, so she didn't start with an initial amount.
• Option C: $m_{Maya}=22$ and $m_{Victor}=20$, they are not saving at the same rate.
• Option D: Maya's relationship is not proportional because when $x = 0$, she has some money saved (not in the form $y=kx$ where $y(0)=0$).

Answer:

A. Both Allie and Maya are saving money at the same rate.