Answer:
Option (2)
Step-by-step explanation:
Table given in the question shows the relation between the size of tank (x) and cost of gas to fill the tank f(x).
Since, relation is a linear function in the form of f(x) = mx + b
Graph of the function will be straight line.
Here 'm' = slope of the line
b = y-intercept
Since, two points (9, 23.55) and (15, 36.75) lie on this line.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{36.75-23.55}{15-9}[/tex]
= [tex]\frac{13.2}{6}[/tex]
= 2.2
By substituting the value of 'm' in the equation,
f(x) = 2.2x + b
Since, the given line passes through (9, 23.55),
23.55 = 2.2(9) + b
b = 23.55 - 19.8
b = 3.75
Equation of the function will be,
f(x) = 2.2x + 3.75
Cost to fill the tank and a car wash with size of the tank = 25 gallons,
f(25) = 2.2(25) + 3.75
= 55 + 3.75
= $58.75
Therefore, Option (2) will be the answer.
