Question

A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon, whereas they sell 3902 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses gallons sold as a function of price. (Hint: express the given information as two ordered pairs, and then find the equation of the line that goes through the two points.) Use this function to predict the number of gallons sold at a price of $1.22 per gallon.

Answer 1

The linear function that expresses gallons sold as a function of price is
`y=-18360x+29606`.

The number of gallons sold at a price of $1.22 per gallon is 7206.8

Explanation:

Consider the provided information.

A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon,

They sell 3902 gallons on a day that they charge $1.40 per gallon.

Let x represents the price per gallon and y represents the number of gallons sold.

Thus the ordered pairs are (1.35,4820) and (1.40,3902)

Now find the slope of line using the formula:
`m=(y_2-y_1)/(x_2-x_1)`

`m=(3902-4820)/(1.40-1.35)`

`m=(-918)/(0.05)`

`m=-18360`

Now find the slope intercept as shown:

`(y-y_1)=m(x-x_1)`

`(y-4820)=-18360(x-1.35)`

`y=-18360x+24786+4820`

`y=-18360x+29606`

Hence, the linear function that expresses gallons sold as a function of price is
`y=-18360x+29606`.

The number of gallons sold at a price of $1.22 per gallon.

Substitute x=1.22 in above equation.

`y=-18360(1.22)+29606`

`y=-22399.2+29606`

`y=7206.8`

Hence, the number of gallons sold at a price of $1.22 per gallon is 7206.8