Question

leveled practice for 6 and 7, complete the information to compare the

1. sam and bobby want to know who cycled faster. the table

shows the total miles sam traveled over time. the
graph shows the same relationship for bobby. who
cycled faster?
find the unit rate (constant of proportionality) for sam.
distance/time = 20/2 = miles/hour
find the unit rate (constant of proportionality) for bobby.
use ( , ) and ( , ) to find the constant
of proportionality.
the unit rate (constant of proportionality) is miles/hour.
so cycled faster.

1. model with math the equation y = 15x can be used to determine

the amount of money, y, paulis pizzeria makes by selling x pizzas.
the graph shows the money leos pizzeria takes in for different
numbers of pizzas sold. which pizzeria makes more money
per pizza?
paulis pizzeria takes in per pizza.
leos pizzeria takes in per pizza.
s pizzeria takes in more money per pizza.

1. the graph shows the amount of savings over time in elianas account.

lana, meanwhile, puts $50 of savings each week into her savings account.
if they both begin with $0, who is saving at the greater rate?

Explanation:

Step1: Calculate Sam's unit - rate

The formula for the unit rate (speed) is $\frac{\text{distance}}{\text{time}}$. Given $\frac{\text{distance}}{\text{time}}=\frac{20}{2}$, we simplify the fraction: $\frac{20}{2} = 10$ miles per hour.

Step2: Calculate Bobby's unit - rate (assuming two points on the graph $(x_1,y_1)$ and $(x_2,y_2)$)

Let's assume two points on Bobby's graph are $(1,12)$ and $(2,24)$ (since for a proportional relationship $y = kx$ and the unit rate $k=\frac{y_2 - y_1}{x_2 - x_1}$). Then $k=\frac{24 - 12}{2 - 1}=\frac{12}{1}=12$ miles per hour.

Step3: Compare the unit - rates

Since $12>10$, Bobby cycled faster.

Step4: For Pauli's Pizzeria

The equation for Pauli's Pizzeria is $y = 15x$, where $y$ is the money and $x$ is the number of pizzas. The coefficient of $x$ is the amount of money per pizza. So Pauli's Pizzeria takes in 15 dollars per pizza.

Step5: For Leo's Pizzeria (assuming two points on the graph $(x_1,y_1)$ and $(x_2,y_2)$)

Let's assume two points on Leo's graph are $(1,10)$ and $(2,20)$. Then the unit rate (money per pizza) is $\frac{20 - 10}{2 - 1}=10$ dollars per pizza.

Step6: Compare the money per pizza

Since $15>10$, Pauli's Pizzeria takes in more money per pizza.

Answer:

For question 6: Sam's unit rate: 10; For Bobby, use (1,12) and (2,24); Bobby's unit rate: 12; Bobby
For question 7: Pauli's Pizzeria: 15; Leo's Pizzeria: 10; Pauli