Word Problems/finding point slope equation in application
In 1982 the annual sales of CDs was 5.8 million. This number roughly increased at a rate of 4.2 million CDs per year.
~ Find an equation in point slope form that models this data, where y represents the number of CDs sold in the year x.
Here rate of increase is constant which is 4.2 million. First year sales is 5.8 million and it is increasing linearly after that. Hence 5.8 will be the constant to which 4.2 will get added each year.
This will generate a straight line whose equation is given by y = mx+c where c is the constant (intercept) and m is the slope (linear increase each year).
With this, our equation becomes,
y = 4.2x + 5.8
However, please note that since data is available from first year (1982), we consider it as x = 0 and will increment x by 1 for each each afterwards. e.g. x = 1 for 1983, x=2 for 1984 etc.
If you need detailed mathematics, then please let me know.
I hope that this helps.