Question 810373
Point-Slope form comes from definition of slope.  If given points (u,v) and (x,y), then slope, {{{highlight(m=(y-v)/(x-u))}}} in which the known point may be (u,v).
Solving that equation for y,
{{{m(x-u)=y-v}}}
{{{y=m(x-u)+v}}}
{{{y=mx-um+v}}}
{{{y=mx+v-um}}}
{{{highlight(y=mx+(v-um))}}} which is in slope-intercept form, for some given point (u,v) on the line.
The slope, m.   The y-intercept, v-mu.