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 $m= \frac{y_{2}-y _{1} }{ x_{2} - x_{1} }$. since we already found those values, lets replace them to find our slope:
$m= \frac{6022-5730}{7-5}$
$m= \frac{292}{2}$
$m=146$

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 $y=146x+5000$