Find the equation of a line that is parallel to line g that contains (P, Q). 3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P

x - y = P - Q

Explanation:

The equation of the line that is parallel to line g, will have the same slope as line g.

Find the slope of line g using two points on the line, (-3, 2) and (0, 5):

m = 1

Point-slope equation takes the form, y - b = m(x - a), where,

(a, b) is a point the line passes through

m = slope of the line

If the line parallel to g passes through (P, Q), then the equation can be written as follows:

Substitute (a, b) = (P, Q), and m = 1 into y - b = m(x - a).

Thus:

y - Q = 1(x - P)

y - Q = x - P

Rewrite

P - Q = x - y

x - y = P - Q