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 large pizza with 5 toppings? round to the nearest penny. $19.00 $22.75 $70.00 $43.75

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 function

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

Step3: Calculate the cost for 5 toppings

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

Answer:

\$22.75