Yes, but not at the level of mathematics you are at.
In elementary statistics, the line of best fit (if it exists) is always a straight line representing a linear relationship between two variables. The equation of the line is most often calculated using the least squares method. [This minimises the sum of the squares of the vertical differences between the values "predicted" by the line and those actually recorded. The process always leads to a straight line.
However, in more advanced statistics, you will learn about transformations. If the relationship between two variables, X and Y, is an inverse relationship, then the relationship between 1/X and Y is linear and you can fit a linear best fit line to the data set given by 1/X and Y. This can then be used to calculate the best fit inverse curve.
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Yes but phrased differently
A line of best-fit.
Because the "best fit" line is usually required to be a straight line, but the data points are not all on one straight line. (If they were, then the best-fit line would be a real no-brainer.)
Finding the line of best fit is called linear regression.
A best-fit line is the straight line which most accurately represents a set of data/points. It is defined as the line that is the smallest average distance from the data/points. Refer to the related links for an illustration of a best fit line.