Question

1. a popular pizza parlor charges $10 for a large cheese pizza plus $2 for each additional topping.

a) what an equation in slope - intercept form for the total cost c of a pizza with t toppings?
b) what is the constant for this function?
c) what is the rate of change?

Explanation:

Part A

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). In this problem, the total cost $C$ depends on the number of toppings $t$. The initial cost (when $t = 0$, i.e., a cheese pizza) is $\$10$, so $b = 10$. The cost per additional topping is $\$2$, so the slope $m = 2$.

Step2: Write the equation

Substituting $m = 2$ and $b = 10$ into the slope - intercept form $y=mx + b$ (where $y = C$ and $x = t$), we get the equation $C=2t + 10$.

Part B

Step1: Identify the constant

In the linear function $C = 2t+10$, the constant (the term that does not depend on the number of toppings $t$) is the initial cost of the pizza.

Step2: Determine the value of the constant

Since the cost of a cheese pizza (with 0 toppings) is $\$10$, the constant in the function $C = 2t + 10$ is $10$.

Part C

Step1: Recall the definition of rate of change

For a linear function of the form $y=mx + b$, the rate of change is the slope $m$.

Step2: Identify the rate of change from the equation

From the equation $C = 2t+10$, which is in the form $y=mx + b$ (where $y = C$, $x = t$, $m = 2$ and $b = 10$), the rate of change (slope) is $2$. This means that for each additional topping, the cost of the pizza increases by $\$2$.

Part A Answer: $C = 2t+10$

Part B Answer: $10$

Part C Answer: $2$

Answer:

Step1: Recall the definition of rate of change

For a linear function of the form $y=mx + b$, the rate of change is the slope $m$.

Step2: Identify the rate of change from the equation

From the equation $C = 2t+10$, which is in the form $y=mx + b$ (where $y = C$, $x = t$, $m = 2$ and $b = 10$), the rate of change (slope) is $2$. This means that for each additional topping, the cost of the pizza increases by $\$2$.

Part A Answer: $C = 2t+10$

Part B Answer: $10$

Part C Answer: $2$