Question

WORTH 30 POINTS

The equation of the line L, is y=3x-2 The equation of the line L, is 3y-9x+5=0 Show that these two lines are parallel.​

Answer 1

Two lines are parallel when they have the same gradient, thus we must prove that these two lines DO.

Y = mx + c, with c being the y-intercept and m being the gradient. Line L1 has a gradient of 3, therefore.

3y-9x+5=0

If we DIVIDE BY THREE — y-3x+5/3=0

Now we must rearrange line L2 to show the gradient of line L2 is also 3. Therefore we must move y to one side and everything else to the other. First, we minus the 5/3 from both sides to give us: y-3x=-5/3

Finally, we add 3x to both sides : y=3x -5/3

As y = mx + c, the gradient of line L2 is also three. As the gradients are equal, the two lines are parallel.