Can be written: 3y=x-6 or y=⅓x-2 (slope=⅓, y-intercept=-2).
You need two points to find the slope. When x=5 in y=⅓x-2, y=-⅓, so (5,-⅓) lies on the line y=⅓x-2. Also, (3,-1) lies on the same line.
(5,-1) doesn't lie on the line. To find the line parallel to y=⅓x-2 which passes through (5,-1) we use the same gradient:
y=⅓x+a where a is the y-intercept of the parallel line.
-1=5/3+a (plugging in (5,-1))⇒a=-1-5/3=-8/3=-2⅔, making the line y=⅓(x-8) (slope=⅓, y-intercept=-8/3).