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. $19.00 $22.75 $43.75 $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. $19.00 $22.75 $43.75 $70.00

Answer

Answer:

$22.75$

Explanation:

Step1: Find the slope of the linear - function

The two points are $(0,14)$ (no toppings, cost $14$) and $(2,17.5)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 14,x_2 = 2,y_2 = 17.5$. So $m=\frac{17.5 - 14}{2-0}=\frac{3.5}{2}=1.75$.

Step2: Find the equation of the line

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

Step3: Find the cost for 5 toppings

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