Question

After 5 months, the number of subscribers to a newspaper was 5,730. After 7 months, the number of subscribers to the newspaper was 6,022. Which equation models the number of newspaper subscribers y after x months? y = –146x – 5,000 y = 146x + 5,000 y = 146x – 5,000 y = –146x + 5,000

Answer 1

From the information given in the problem we can create a linear model like this: The
`x-axis` will represent the months and the
`y-axis` the subscribers. From the problem we know that after 5 months, the number of subscribers to a newspaper was 5,730, so
`x_(1) =7` and
`y_(1) =5730`. We also know that after 7 months, the number of subscribers to the newspaper was 6,022, so
`x_(2) =7` and
`y_(2) =6022`.
Remember that the slope of a line is
`m= (y_(2)-y _(1) )/( x_(2) - x_(1) )`. since we already found those values, lets replace them to find our slope:

`m= (6022-5730)/(7-5)`

`m= (292)/(2)`

`m=146`

To create our linear model we are going to use the point-slope equation
`y- y _(1) =m(x- x_(1) )`. Notice that we have all the values, so the only thing left is plug them in our equation:

`y-6022=146(x-5)`

`y-5730=146x-730`

`y=146x-730+5730`

`y=146x+5000`

We can conclude that the equation which models the number of newspaper subscribers
`y` after
`x` months is
`y=146x+5000`