Respuesta :
Answer:
[tex]C=18w+30[/tex]
Step-by-step explanation:
We are given that The monthly charge for a waste collection service is 1830 dollars for 100 kg of waste
So, [tex](x_1,y_1)=(100,1830)[/tex]
We are also given that The monthly charge for a waste collection service is 2460 dollars for 135 kg of waste.
So, [tex](x_2,y_2)=(135,2460)[/tex]
We are supposed to find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w.
So, we will use two point slope form :
Formula : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the values
[tex]y-1830=\frac{2460-1830}{135-100}(x-100)[/tex]
[tex]y-1830=18(x-100)[/tex]
[tex]y-1830=18x-1800[/tex]
[tex]y=18x-1800+1830[/tex]
[tex]y=18x+30[/tex]
y denotes the cost
x denotes the weight
So, Replace y with C and x with w
[tex]C=18w+30[/tex]
So, a linear model for the cost, C, of waste collection as a function of the number of kilograms, w is [tex]C=18w+30[/tex]
