Question

the cost in dollars, y, of a large pizza with x toppings from pats pizzeria can be modeled by a linear function. a large pizza with no toppings costs $14.00. a large pizza with 2 toppings costs $17.50. what is the cost of a pizza with 5 toppings? round to the nearest penny. $19.00 $22.75 $43.75 $70.00

Explanation:

Step1: Define linear function

Let the linear function be $y = mx + b$, where $m$ is the cost per topping, $b$ is the base cost (no toppings), $x$ is the number of toppings, and $y$ is total cost.

Step2: Plug in known values

For 0 toppings: $14.00 = m(0) + b$, so $b = 14.00$.
For 2 toppings: $17.50 = m(2) + 14.00$

Step3: Solve for m

Rearrange to solve for $m$:
$2m = 17.50 - 14.00$
$2m = 3.50$
$m = \frac{3.50}{2} = 1.75$

Step4: Calculate cost for 5 toppings

Substitute $x=5$, $m=1.75$, $b=14.00$ into $y=mx+b$:
$y = (1.75)(5) + 14.00$
$y = 8.75 + 14.00 = 22.75$

Answer:

$22.75$ (Option: $22.75$)