Question

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matching: for each situation below, determine which equation best represents the relationship between x and y.
answer bank: ( y = 8x ) ( y=\frac{1}{8}x ) ( y = x + 8 ) ( y = x - 8 )

1. a comparison of siblings ages:

comparison of sibling ages
graph of arjuns age (years) vs mateos age (years) with x from 1 to 8 and y from 1 to 16, data points at (1,9), (2,10), (3,11), (4,12), (5,13), (6,14)

1. a student earns $8 per hour while helping a neighbor weed their garden.
2. transportation needs for a field trip:

field trip transportation

number of students, x	8	16	32	40
number of vans, y	1	2	4	5

1. you have a coupon for $8 off your total bill at a frozen yogurt shop.

Explanation:

Step1: Analyze sibling age graph

Take points from the graph: when $x=1$, $y=9$; $x=2$, $y=10$; $x=3$, $y=11$. Calculate the difference: $y - x = 8$, so $y=x+8$.

Step2: Analyze hourly earnings

Total earnings $y$ = hourly rate $\times$ hours $x$. Rate is $8$, so $y=8x$.

Step3: Analyze field trip table

Check ratios: $\frac{y}{x}=\frac{1}{8}$, $\frac{2}{16}=\frac{1}{8}$, so $y=\frac{1}{8}x$.

Step4: Analyze coupon discount

Final bill $y$ = original bill $x$ - $8$, so $y=x-8$.

Answer:

1. $y = x + 8$
2. $y = 8x$
3. $y = \frac{1}{8}x$
4. $y = x - 8$