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.

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Answered by Anca I. Maths tutor

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