It's a matter of definition. There are perhaps a dozen useful forms of equations for a line. Each has its own name (and use). Here are some of them.
slope-intercept form: y = mx + b
point-slope form: y -y1 = m(x -x1)
two-point form: y = (y2-y1)/(x2-x1)(x -x1) +y1
intercept form: x/a +y/b = 1
standard form: ax +by = c
general form: ax +by +c = 0
Adding y1 to the point-slope form puts it in an alternate form that is useful for getting to slope-intercept form faster: y = m(x -x1) +y1. I use this when asked to write the equation of a line with given slope through a point, with the result in slope-intercept form.
