Equation of a Straight Line

Question

The equation of line L is y=2x+1

The equation of line L2 is 4y-8x+1=0

Show that these two lines are parallel.

Please help me with this question.

Answer 1

solve L2 for y

4y-8x +1 = 0

4y = 8x +1

y = 8x/4 +1/4

y = 2x +1/4

L2's slope =2, the coefficient of the x term, when the equation is solved for y

L also has slope =2, the coefficent of the x term y=2x+1

if two lines have the same slope and different y intercepts, they are parallel

L has y intercept =1 = the constant term

L2 has y intercept = 1/4

if the y intercepts had been the same, the two lines would have been identical, the same line and not parallel