Select the equations of the lines that are parallel to the line whose equation is y = 3x + 5.

6x + 2y = 12

-3x + y = 8

3y = 9x

y = - x

The slope-intercept form of the equation of a straight line:

y=mx+b

m=slope

Therefore; in this equation (y=3x+5); m=3

a)

6x+2y=12

2y=-6x+12

y=-6/2 x + 12/2

y=-3x+6 ⇒ m=-3≠3 (this line is not parallel to "y=3x+5")

b)

-3x+y=8

y=3x+8 ⇒ m=3 (this line es parallel to "y=3x+5")

c)

3y=9x

y=9/3 x

y=3x ⇒ m=3 (this line is parallel to "y=3x+5")

d)

y=-x ⇒ m=-1≠3 (this line is not parallet to "y=3x+5")

Therefore; "-3x+y=8" and "3y=9x" are parallel to "y=3x+5".