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: Find the slope of the linear function

The linear function is in the form \( y = mx + b \), where \( b \) is the y - intercept (cost when \( x = 0 \)) and \( m \) is the slope (cost per topping). We know that when \( x = 0 \), \( y=14 \), so \( b = 14 \). When \( x = 2 \), \( y = 17.5 \). 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

Using \( y=mx + b \) with \( m = 1.75 \) and \( b = 14 \), the equation is \( y=1.75x + 14 \).

Step3: Calculate the cost for \( x = 5 \) toppings

Substitute \( x = 5 \) into the equation: \( y=1.75\times5+14 \). First, calculate \( 1.75\times5 = 8.75 \). Then, \( y=8.75 + 14=22.75 \).

Answer:

$22.75$