Question

The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month.Minutes: 500, 750, 1000, 1250, 1500 Total Monthly cost (in dollars): $62, $77, $92, $107, $122 Choose the correct linear model that represents the total monthly cost as a function of time.These are your optionsy = 0.06x + 500y = 16x + 32 y = 62x + 32y = 0.06x + 32

Answer 1

Given that the relationship between the total cost and number of minutes is linear, we would write it in the slope intercept form which is expressed as

y = mx + c

where

m represents slope

c represents y intercept

The formula for calculating slope is expressed as

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

In this scenario, the x values are the number of minutes while the y values are the total cost. From the table,

when x1 = 500, y1 = 62

when x2 = 750, y2 = 77

Substituting theses values into the slope formula, we have

m = (77 - 62)/(750 - 500) = 15/250 = 0.06

We would find the y intercept by substituting m = 0.06, x = 500 and y = 62 into the slope intercept equation. We have

62 = 0.06* 500 + c

62 = 30 + c

c = 62 - 30 = 32

By substituting m = 0.06 and c = 32 into the slope intercept equation, the correct linear model that represents the total monthly cost as a function of time is

y = 0.06x + 32