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.

Two lines are parallel if they have the same gradient. This can be found by looking at the coefficient of x. When the equation is written in the form y=ax+b, with b a constant, the gradient of the line would be a. So for the L₁ the gradient is 3. So we want to get L₂ in this form as well we rearrange L₂, to 3y = 9x - 5, and then divide by 3 to get y = 3x -5/3. So the gradient of L₂ is also 3 and therefore both lines are parallel.