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
To find the linear function that models the cost of a large pizza with x toppings, we can use the information given:
When there are no toppings (x = 0), the cost is $14.00.
When there are 2 toppings (x = 2), the cost is $17.50.
Let's create the linear function in slope-intercept form: y = mx + b, where y is the cost of the pizza and x is the number of toppings.
We can find the slope (m) using the given information. The change in the number of toppings from 0 to 2 is 2 - 0 = 2, and the change in the cost from $14.00 to $17.50 is $17.50 - $14.00 = $3.50.
m = (change in cost) / (change in toppings) = $3.50 / 2 = $1.75.
Now, let's find the y-intercept (b) by substituting the values of one of the points (x, y) into the equation.
Using the point (0, $14.00):
14 = (1.75)(0) + b
14 = 0 + b
b = 14.
So, the linear function that models the cost of a large pizza with x toppings is y = 1.75x + 14.
Now plug in x = 5 to find the cost of a pizza with 5 toppings:
y = 1.75(5) + 14
y = $8.75 + $14
y = $22.75.
Therefore, the cost of a pizza with 5 toppings is approximately $22.75.