Question

direct variation performance task
a gallon of gas costs $2.25 at your local gas station.

1. does the cost of filling up your car with gas vary directly with the number of gallons of gasoline you are purchasing? explain your reasoning.
2. create a table of values for the cost of the first 5 gallons of gas that you purchase.

number of gallons

total cost

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1. choose one entry from your table and explain what it means in the context of the problem.

Explanation:

Step1: Define direct variation

Direct variation is of the form $y = kx$, where $k$ is a non - zero constant. Here, let $y$ be the total cost and $x$ be the number of gallons. The cost per gallon $k = 2.25$.

Step2: Answer question 1

Since the total cost $y$ of gas is given by $y=2.25x$ (where $x$ is the number of gallons), the cost of filling up the car with gas varies directly with the number of gallons of gasoline purchased because the ratio of the total cost to the number of gallons is always the constant price per gallon ($2.25$).

Step3: Create table for question 2

Number of Gallons	Total Cost
2	$2.25\times2 = 4.50$
3	$2.25\times3 = 6.75$
4	$2.25\times4 = 9.00$
5	$2.25\times5 = 11.25$

Step4: Explain an entry for question 3

Let's take the entry for 3 gallons. When $x = 3$ (number of gallons), $y=6.75$ (total cost). This means that when you purchase 3 gallons of gas at a price of $2.25$ per gallon, the total amount of money you will spend is $6.75$.

Answer:

1. Yes, because the total cost $y$ and number of gallons $x$ follow the relationship $y = 2.25x$, where 2.25 is the constant of variation (price per gallon).

2.

Number of Gallons	Total Cost
2	$4.50$
3	$6.75$
4	$9.00$
5	$11.25$

1. For example, when the number of gallons is 3 and the total cost is $6.75$, it means that purchasing 3 gallons of gas at $2.25$ per gallon costs $6.75$.