Question

leveled practice for 6 and 7, complete the information to compare the rates. 6. 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. $\frac{distance}{time}=\frac{20}{2}=\frac{10}{1}\frac{miles}{hour}$ find the unit rate (constant of proportionality) for bobby. use ( , ) and ( , ) to find the constant of proportionality. the unit rate (constant of proportionality) is $\frac{miles}{hour}$. so cycled faster. 7. model with math the equation $y = 15x$ can be used to determine the amount of money, y, pauli’s pizzeria makes by selling x pizzas. the graph shows the money leo’s pizzeria takes in for different numbers of pizzas sold. which pizzeria makes more money per pizza? pauli’s pizzeria takes in per pizza. leo’s pizzeria takes in per pizza. ’s pizzeria takes in more money per pizza. 8. the graph shows the amount of savings over time in eliana’s account. lana, meanwhile, puts $50 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 unit rate (constant of proportionality) for Sam is found by dividing the distance by the time. Given that Sam travels 20 miles in 2 hours, the unit rate $r_{Sam}=\frac{20}{2}=10$ miles per hour.

Step2: Calculate Bobby's unit - rate

For Bobby, we can use two points on the line. Let's use the points $(2,36)$ and $(4,72)$ (we can choose any two non - overlapping points on the straight - line graph). The unit rate (constant of proportionality) $r_{Bobby}=\frac{y_2 - y_1}{x_2 - x_1}=\frac{72 - 36}{4 - 2}=\frac{36}{2}=18$ miles per hour.
Since $18>10$, Bobby cycled faster.

Step3: Calculate Pauli's Pizzeria's money per pizza

For Pauli's Pizzeria, the equation is $y = 15x$, where $y$ is the money made and $x$ is the number of pizzas sold. The unit rate (money per pizza) is 15 dollars per pizza.

Step4: Calculate Leo's Pizzeria's money per pizza

For Leo's Pizzeria, if we use the points $(2,48)$ and $(4,96)$ on the line, the unit rate (money per pizza) $r_{Leo}=\frac{96 - 48}{4 - 2}=\frac{48}{2}=24$ dollars per pizza.
Since $24>15$, Leo's Pizzeria makes more money per pizza.

Step5: Calculate Eliana's savings rate

For Eliana, using the points $(2,188)$ and $(4,376)$ on the line, the savings rate $r_{Eliana}=\frac{376 - 188}{4 - 2}=\frac{188}{2}=94$ dollars per week.
Lana saves 50 dollars per week. Since $94>50$, Eliana is saving at a greater rate.

Answer:

1. Use $(2,36)$ and $(4,72)$; 18; Bobby
2. 15; 24; Leo
3. Eliana