Question

Choose the correct way to end the sentence.The lines x – 2y = 4 and y = 2x – 2 areA. parallelB. neitherC. perpendicular

Answer 1

Given the equations of the lines:

$\begin{gathered} x-2y=4\rightarrow(1) \\ y=2x-2\rightarrow(2) \end{gathered}$

We will write both equations in slope-intercept form to find the slope of each line:

The equation of the first line:

$\begin{gathered} x-2y=4 \\ -2y=-x+4\rightarrow(\div-2) \\ \\ y=\frac{1}{2}x-2 \end{gathered}$

so, the slope of the line (1) = 1/2

the equation of the second line:

$y=2x-2$

so, the slope of the second line = 2

Comparing the slopes of the lines:

1) the slopes are not equal, so the lines are not parallel

2) the product of the slopes = 1/2 * 2 = 1

So, the lines are not perpendicular

so, the answer will be option B. neither