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HELP PLEASE!! The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. The costs of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallons.

HELP PLEASE The cost to fill a cars tank with gas and get a car wash is a linear function of the capacity of the tank The costs of a fillup and a car wash for t class=

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For this case we have a linear function of form:

[tex]y = f (x)[/tex]

Where: [tex]f (x) = mx + b[/tex]

y: Represents the total cost of filling and washing

m: Represents the cost of filling the tank of a car with gasoline

[tex]m = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]

x: Represents the capacity of the tank

b: Represents the cost of car washing

To find the slope, we need two points. Be:

[tex](x_ {1}, y_ {1}) = (9,22.15)\\(x_ {2}, y_ {2}) = (16,36.85)[/tex]

Substituting in the formula of the slope, we have:

[tex]m = \frac {36.85-22.15} {16-9}[/tex]

[tex]m = \frac {14.7} {7}[/tex]

[tex]m = 2.1[/tex]

To find the cost of the car wash, that is, "b", we substitute the slope and any of the points in the equation [tex]y = mx + b[/tex]:

[tex]22.15 = 2.1 (9) + b\\22.15 = 18.9 + b\\b = 22.15-18.9\\b = 3.25[/tex]

Thus, the cost of a fill-up and a car wash for a customer is: [tex]f (x) = 2.1x + 3.25[/tex], where x represents the tank capacity of the car to be treated.

If the tank capacity of the truck is 25 gallons, we substitute[tex]x = 25.[/tex]

[tex]f (25) = 2.1 (25) +3.25\\f (25) = 52.5 + 3.25\\f (25) = 55.75[/tex]

Thus, the total cost to fill and wash the truck is 55.75 dollars.

Answer:

[tex]f (x) = 2.1x + 3.25\\f (25) = 55.75[/tex]

Option A

The cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallons is [tex]\$55.75[/tex]

An equation for the function in slope-intercept form is,

[tex]y=mx+b\\Let \;y=f(x)[/tex]--------1

[tex]y=[/tex] Represent the total cost of filling and washing

[tex]m:[/tex]Represent the cost of filling the tank of a car with gasoline.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Tank size is [tex]x[/tex]

Cost of car wash is [tex]b[/tex]

Total cost[tex](\$)=f(x)[/tex]

[tex](x_1,y_1)=(9,22.15)\\\\(x_2,y_2)=(16,36.85)\\\\(x_3,y_3)=(16,36.85)[/tex]

Find value of slope i.e, [tex]m[/tex]

[tex]m=\dfrac{36.85-22.15}{16-9}\\\\m=\dfrac{14.7}{7}\\\\m=2.1[/tex]

Find Cost of Car wash

Put value in eq 1

[tex]22.15=2.1(9)+b[/tex]

[tex]b=22.15-18.9\\b=3.25[/tex]

Hence, equation for the function in slope-intercept form is ,

[tex]f(x)=2.1+3.25[/tex]

Now if the tank capacity is [tex]25[/tex] gallons ,

[tex]f(25)=2.1(25)+3.25\\f(25)=52.5+3.25\\f(25)=55.75[/tex]

Hence, the cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallon is [tex]\$55.75[/tex]

Learn more about slope form here:

https://brainly.com/question/18491580?referrer=searchResults

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