in slope-intercept form, what is the equation of the line passing through (6,22) and parallel to the line joining (11,3) and (2,6)

Answer 1

The slope of the second line you mentioned is
(y2-y1)/(x2-x1) = (6-3)/(2-11) = -1/3

Therefore you are looking for a line which passes through (6,22) with slope -1/3.

That would be (y - 22) = (-1/3)(x-6)
which can be rewritten
y = (-x/3) + 24