What is the y - y1 = m(x - x1) equation of a line based on (derived from)? explain how this is done.

Hello!!

y-y1=m(x-x1) is the point slope form of a line. Where m=slope. So by dividing by (x-x1) on both sides we get m=(Y2-Y1)/(X2-X1) which defines slope of the line. Then we can plug two arbitrary points from our line in for the y and x values and then solve for m. Then it can be put it into slope-intercept form, which is y=mx+b where x and y are any coordinate points on the line, and m is your slope of that line, and b is the y-intercept or where the line crosses the y-axis when x=0. 

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