Question

you are given a cell phone bill. You are charged $52 for the month. There is a $40 monthly fee and you are charged $4 per megabyte of data used.

Construct a linear equation for this model

What is the value of the y-intercept? What does it mean?

What is the value of the slope? What does it mean?

If you use 10 megabytes of data how much would you expect to pay for your bill?

Where else might you use this type of model? Be specific.

Answer 1

(1) As there is $40 fixed fee for every month so this will be known as Fixed Cost per month of mobile data.

Also for each MB(megabytes) we have to pay $4 as this cost depends on number of MB data we used so it is known as variable cost.

Let x be number of units of MB of data we used in a month then Linear Equation will be

y=f(x)=4x+40

(2) For y-intercept we have to put x=0 in our linear model

Therefor

y-intercept is

y=f(0)=4(0)+40=40

It means the minimum amount of bill we have to oay every month.

So either we use data or not we have to pay atleast $40 bill.

This is the monthly bill when we used 0 MB of data.

(3) For the linear model in standard form

y=mx+c

m-is known as slope.

Here y=4x+40

Hence slope is 4.

Slope means the rate of change at which our quantity in changing (increasing or decreasing)

Here our bill is increasing at rate of $4 per unit of MB.

(4) When we use 10 MB of data then bill will be

y at x=10

f(10)=4(10)+40=40+40=$80

(5) We use this linear model when there is only one dependent variable and one independent variable like bill for a single product(gas bill,electricity bill)

Expences of our car by using Diesel/Petrol price as variable cost and a fix amount of maintainence as fixed cost.