Answer:
The linear function that expresses gallons sold as a function of price is [tex]y=-18360x+29606[/tex].
The number of gallons sold at a price of $1.22 per gallon is 7206.8
Step-by-step 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: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3902-4820}{1.40-1.35}[/tex]
[tex]m=\frac{-918}{0.05}[/tex]
[tex]m=-18360[/tex]
Now find the slope intercept as shown:
[tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-4820)=-18360(x-1.35)[/tex]
[tex]y=-18360x+24786+4820[/tex]
[tex]y=-18360x+29606[/tex]
Hence, the linear function that expresses gallons sold as a function of price is [tex]y=-18360x+29606[/tex].
The number of gallons sold at a price of $1.22 per gallon.
Substitute x=1.22 in above equation.
[tex]y=-18360(1.22)+29606[/tex]
[tex]y=-22399.2+29606[/tex]
[tex]y=7206.8[/tex]
Hence, the number of gallons sold at a price of $1.22 per gallon is 7206.8
