When it is easier to use the point-slope form to write the equation of a line and when it is easier to use the slope-intercept form?

It is easier to use point-slope form when we have two points to write the equation from.
It is easier to use slope-intercept form when we have the slope and the y-intercept.

Point-slope form is given by y-y₁=m(x-x₁).  We use the formula m=(y₂-y₁)/(x₂-x₁) to find the slope; we use two points to do this.  Then we use one of the points to write it in point-slope form.

Slope-intercept form is given by y=mx+b; we need the slope, m, and the y-intercept, b, to use this form.