the cost in dollars, y, of a large pizza with x toppings from pats pizzeria can be modeled by a linear…

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.\n$19.00\n$22.75\n$43.75\n$70.00

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.\n$19.00\n$22.75\n$43.75\n$70.00

Answer

Answer:

B. $$22.75$

Explanation:

Step1: Find the slope of the linear function

The two - point form of a line is $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. We have the points $(x_1,y_1)=(0,14)$ (no toppings, cost $14$) and $(x_2,y_2)=(2,17.5)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{17.5 - 14}{2-0}=\frac{3.5}{2}=1.75$.

Step2: Write the linear equation

The slope - intercept form of a line is $y=mx + b$, where $b$ is the $y$ - intercept. Since when $x = 0$, $y = 14$, $b = 14$. So the equation is $y=1.75x+14$.

Step3: Find the cost for 5 toppings

Substitute $x = 5$ into the equation $y=1.75x + 14$. Then $y=1.75\times5+14=8.75 + 14=22.75$.