Justin is taking a taxi cab to pick up his car from the auto shop. The taxi charges an initial fee of $5.00 and additional $2.50 for each mile the taxi drives. Write an equation using x as the number of miles, to determine how many miles the taxi drove if Justin spent $25.00. Use your equation for the number of miles. (Define the variable please, write an equation, and solve & label:))

x = 8

Step-by-step explanation:

Given the initial fee of $5.00, and the additional cost of $2.50 for every mile the taxi drives:

We can establish the following cost function:

C(x) = 2.50x + 5.00

Where:

C(x) = total cost of taxi fare (same as the variable, "y" in linear equation)

x = number of miles driven

$5.00 = initial or flat fee (same as the y-intercept, "b," in linear equation).

We can find out the number of x miles the taxi drove for the $25.00 total cost that Justin paid for the fare:

C(x) = 2.50x + 5.00

$25 = 2.50x + 5.00

Subtract 5.00 from both sides of the equation:

$25 - 5.00 = 2.50x + 5.00 - 5.00

$20 = 2.50x

Divide both sides by 2.50 to solve for x:

8 = x

Justin spent $25 for a taxi ride that travelled for 8 miles.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: