The equation of the line L1 is y = 3x – 2. The equation of the line L2 is 3y – 9x + 5 = 0. Show that these two lines are parallel.

To begin with,for every line ax+by+c=0 the gradient is m=(-a)/b.From theory, it is known that two lines are parallel only if their gradients are equal. For line 1: y=3x-2, it implies that 3x-y-2=0(we just subtract the y into the opposite part).This means that line 1 gradient is equal to m₁=-(3)/(-1) => m₁=3.For line 2 : 3y-9x+5=0 the gradient m₂=-(-9)/3 =>m₂=3 .Since m₁ is equal to m₂ ,then the 2 lines are parallel.