This straightforward method is called a linear scale or curve formula. It is a very versatile way of using a curve and can be used to give an extra boost to the weakest students and can be used to adjust the mean to be a target value.

This Excel sheet does all the "math" for you. If you need to justify its use to students or administrators, the Excel file explains and shows the formula being used.

I use linear curves for all my advanced or challenging assessments. I will pick the highest and lowest raw student scores and decide what grade I want them to become after the curve. These two points determine the linear scale curve.

For example, I often want the grades to have a specific average. So, if the mean of the raw scores is 76%, then (76,80) is one point. Then I may take the low score (or high score) and force it to go somewhere. Say the low score is 58% and I want it to be 64%, I will adjust the Excel sheet to display it.