Question

The monthly charge for a waste collection service is 2248 dollars for 100 kg of waste and 2798 dollars for 125 kg of waste.(a) Find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w.C= ___(b) What is the slope of the line found in part (a)?Slope =(c) What is the value of the vertical intercept of the line found in part (a)?Vertical intercept=

Answer 1

A linear model has the following form:

y = mx + b

Where m is the slope and b is the vertical intercept

The slope of a linear model is calculated by means of the following formula:

`m=(y2-y1)/(x2-x1)`

Where y is the cost and x is the amount of waste, we know that the service cost is 2248 dollars for 100 kg of waste and 2798 dollars for 125 kg of waste, by replacing these values into the above equation we get:

`m=(2798-2248)/(125-100)=(550)/(25)=22`

Then, the slope of the line is 22

By replacing 22 for m into the general model, we can rewrite it to get:

y = 22x + b

By replacing 2798 for y and 125 for x we can solve for b to get:

2798 = 22(125) + b

2798 = 2750 + b

2798 - 2750 = 2750 - 2750 + b

48 = b

b = 48

Then, the vertical intercept of the line is 48

The linear model for the cost, C, of waste collection as a function of the number of kilograms, w would be:

C = 22w + 48