Outliers are no problem

Algebra Level 4

Find the best line to fit the data points $(1,0), (2,0), \ldots, (9,0), (10,40).$ Use the least squares method: the line should be the one that minimizes the sum of the squares of the errors in the $y$ -coordinates.

If the line is written as $y = mx+b,$ where $m =\frac pq$ with $p$ and $q$ being coprime prime positive integers and $b$ is an integer, find $p+q+b.$