Explanation:
the point-slope form is
y - y₁ = m(x - x₁)
with (x₁, y₁) being a given point. "m" is the slope.
now, we know that the given line equation is in slope-intercept form
y = mx + b
"m" is again the slope, "b" is the y-intercept (the y value when x = 0).
so, we know the slope is the original line is -2/3.
a parallel line must have the same slope, of course.
the point-slope form for the parallel line is therefore
y - -5 = (-2/3)(x - 4)
y + 5 = (-2/3)(x - 4)
if we multiply it out and clean things up, we get the corresponding slope-intercept form.