Question

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

Answer 1

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".