the slope intercept form of the equation of a line is of the form:

y = mx + b

where m is the slope and b is the y-intercept.

m = (y2 - y1)/(x2 - x1) = (6 - 4)/(3 + 3) = 2/6 = 1/3

now we can start with the point-slope form and simplify to the slope intercept form. by the point slope form, using m = 1/3 and (x1,y1) = (3,6), we have

y - y1 = m(x - x1)

=> y - 6 = (1/3)(x - 3)

=> y = (1/3)x - 1 + 6

=> y = (1/3)x + 5 ...................slope intercept form