geometry notes for class

Question

what is a slope of a line parallel to a given equation 2x+6y=8

Answer 1

2x + 6y = 8

solve for y

6y = -2x +8

y = -x/3 +4/3

slope = the coefficient of the x term when the linear equation is solved for y, = -1/3

any parallel line has that same slope = -1/3