Use the slope formula $m = (y_2 - y_1)/(x_2 - x_1)$ with $(4,10)$ and $(10,22)$. This slope represents the constant price per taco.

After you know the price per taco, plug it with one point into $C = mt + b$ to solve for the fixed fee $b$.

Once you have both the price per taco and the fixed fee, substitute $t = 8$ into $C = mt + b$ and simplify.

In Desmos, type m = (22 - 10)/(10 - 4) and look at the value of m. This is the constant price per taco (the slope).

On a new line, type b = 10 - 4*m. This uses the point $(4,10)$ to solve for the fixed service fee b based on your m value.

On another line, type C = m*8 + b. The value shown for C is the total cost for 8 tacos according to this linear model; match that value to the closest answer choice.

Let $t$ be the number of tacos and $C$ be the total cost in dollars. Because the pricing is linear with a fixed fee plus a constant price per taco, we can write

where $m$ is the price per taco and $b$ is the fixed service fee. From the problem, we know two points on this line:

• When $t=4$, $C=10$ → the point $(4,10)$
• When $t=10$, $C=22$ → the point $(10,22)$.

Use the two points to find the slope $m$:

Compute the numerator and denominator, then simplify this fraction to find the constant price per taco.

Once you know $m$, plug it into one of the point equations, for example using $(4,10)$:

Solve this equation for $b$ to find the fixed service fee.

Now write the full equation using your values of $m$ and $b$:

Plug in $t = 8$:

Evaluate this expression to get $C = 18$, so the total cost for 8 tacos is \18$, which corresponds to choice C.