Question

Courtney remembers that her ATV has 6gallons of gas in the tank on Monday. She is using gas at a rate of 3gallons for 45miles.A). Write a linear equation that represents the number of "Y" gallons left in the tank after "X" miles.B). Graph the linear equationC). How many gallons will be left after 90miles

Answer 1

Step-by-step explanation:

The reason or proportion that arises in the exercise is:

`\begin{gathered} (y)/(x)=(3)/(45) \\ (3)/(45)=0.066 \\ \text{the constant or porpor}tion\text{ is :0.066} \end{gathered}`

A.Now knowing the constant or proportion we can formulate an equation:

(ANSWER A:)

`\begin{gathered} y=(x)(0.066) \\ \text{where x is }time\text{ in miles }for\text{ the constant} \end{gathered}`

Multiplying any time in miles by the constant will give us the number of gallons consumed in y.

B.Now to graph the linear equation we must give x values ​​to obtain the values ​​for gallons of gas.(ANSWER B)

To have the values ​​in x we ​​can use the ones shown in the graph:

`\begin{gathered} -y=(x)(0.066) \\ y=(5)(0.066) \\ y=0.33 \\ -y=(x)(0.066) \\ y=(10)(0.066) \\ y=0.66 \\ -y=(15)(0.066) \\ y=0.99 \\ -y=(20)(0.066) \\ y=1.32 \\ -y=(25)(0.066) \\ y=1.65 \end{gathered}`

With the previous data we can graph.:

the graph is as follows:

In the graph we can see that as time progresses the gallons of gasoline consumed increases constantly.

C.To find out how many gallons of gasoline are left after 90 miles we must use the equation we found and replace the value of 90 miles in x, so we will know if after that time there is still gasoline.(ANSWER C)

`\begin{gathered} y=(x)(0.066) \\ y=(90\text{ miles})(0.066) \\ y=6\text{ } \\ \text{The answer is }\colon After\text{ 90 miles }all\text{ 6 gallons of gasoline }have\text{ } \\ \text{been used.} \end{gathered}`