Chapter 5.4, Problem 6STP

The table shows the cost of a large cheese pizza with additional toppings on it.

What is an equation in point-slope form that represents the relationship between the number of toppings and the cost of the pizza?

b. What is the graph of the equation?

To determine

To calculate: the relationship between the number of toppings and the cost of the pizza?

Answer to Problem 6STP

The equation is $c=8+1.25*t$ , where $c$ is the cost of pizza with $t$ toppings

Explanation of Solution

Given:

The cost of 3 toppings and 1 pizza is given as $11.75 and the cost of 2 toppings and 1 pizza is given as $10.50

Calculation:

subtracting the above two given value, we get the value of 1 topping

Cost of 1 topping = (cost of 3 toppings and 1 pizza) - (cost of 2 toppings and 1 pizza)

= $11.75-$10.50=$1.25

We know the cost of 1 topping and we also know the cost of 3 toppings and 1 pizza, subtracting cost of 3 toppings from the cost of 3 toppings and 1 pizza we get the cost of 1 pizza. i.e.

cost of 1 pizza = (cost of 3 toppings and 1 pizza) - cost of 3 toppings

  $\begin{array}{l}=\$11.75-3*\$1.25\\ =\$11.75\$-3.75\\ =\$8\end{array}$

Now we can write the equation in point slope form

Let $c$ be the cost of pizza with $t$ toppings, then

  $c=pizzacost+1.25*t$

Here cost of 1 pizza is $8, so

  $c=8+1.25*t$

Conclusion:

The equation is $c=8+1.25*t$ , where $c$ is the cost of pizza with $t$ toppings.

To determine

To graph: The table shows the cost of a large cheese pizza with additional toppings on it. What is the graph of the equation?

  

Explanation of Solution

Given:

From above part we know that the equation is $c=8+1.25*t$ , where $c$ is the cost of pizza with $t$ toppings

Calculation:

$t$	2	3	5
$c=8+1.25*t$	10.5	11.75	14.25

From plotting above values in a graph, we get the graph