Given that,
y = mx + b ...... (1)
then the point-slope form make sense as a name for,
y - y1 = m(x-x1) .......(2)
Equation (1) we get,
y = mx + b
b = y - mx ....... (3)
m is a slope
b is the y-intersect
(x1,y1) is the points
Solve the equation (2),
y - y1 = m(x - x1)
y - y1 = mx - mx1
y = mx - mx1 + y1
y = mx + (y1 - mx1)
y = mx + b ......... (4) (use equation (3))
Therefore we prove the y = mx - b
