Let $r$ be the rate per mile and $b$ be the flat fee. Use the information from the 5-mile ride and the 11-mile ride to write two equations involving $r$ and $b$.

Once you have the two equations, try subtracting one from the other to eliminate $b$ and solve for the rate $r$.

After you find $r$ and $b$, plug them into your cost formula, then substitute $m = 8$ to find the cost of an 8-mile ride.

In Desmos, type (31-19)/(11-5) on a new line. The value that appears is the constant rate per mile.

On the next line, type 19 - 5*(previous_answer) or explicitly 19 - 5*( (31-19)/(11-5) ). The result is the flat fee (the starting cost before any miles are added).

Finally, type 8*( (31-19)/(11-5) ) + ( 19 - 5*( (31-19)/(11-5) ) ). The value Desmos shows is the cost of an 8-mile ride; match this value to the closest answer choice.

Let $m$ be the number of miles and $C$ be the total cost. Because the taxi company charges a flat fee plus a constant rate per mile, we can write

where $r$ is the rate per mile and $b$ is the flat fee. Using the two rides:

• For 5 miles: $19 = 5r + b$
• For 11 miles: $31 = 11r + b$

We have the system:

Subtract the first equation from the second to eliminate $b$:

So the rate per mile is

Now plug $r = 2$ into one of the original equations, for example $19 = 5r + b$:

Subtract 10 from both sides:

So the flat fee is $9.

Now we know the cost equation is

For an 8-mile ride, substitute $m = 8$:

So the cost of an 8-mile ride is $25, which corresponds to choice B.