Question

find and interpret the rate of change and the initial value. 5. a pizzeria charges $8 for a large cheese pizza, plus $2 for each topping. the total cost for a large pizza is given by the equation c = 2t + 8, where t is the number of toppings. graph the equation for t between 0 and 5 toppings, and explain the meaning of the slope and y - intercept.

Explanation:

Step1: Identify the slope - rate of change

The equation is in the form $C = 2t+8$, which is similar to the slope - intercept form $y = mx + b$. Here, the coefficient of $t$ is the slope $m$. The rate of change (slope) is 2. This means that for each additional topping, the cost of the pizza increases by $2.

Step2: Identify the y - intercept - initial value

In the equation $C = 2t + 8$, the constant term is 8. When $t = 0$ (no toppings), the cost $C$ of the pizza is $8. So the initial value (y - intercept) is 8, which is the cost of a large cheese pizza with no toppings.

Answer:

Rate of change: 2. It means the cost increases by $2 per topping.
Initial value: 8. It means the cost of a large cheese pizza with no toppings is $8.