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Given the equations of the lines:
[tex]\begin{gathered} x-2y=4\rightarrow(1) \\ y=2x-2\rightarrow(2) \end{gathered}[/tex]We will write both equations in slope-intercept form to find the slope of each line:
The equation of the first line:
[tex]\begin{gathered} x-2y=4 \\ -2y=-x+4\rightarrow(\div-2) \\ \\ y=\frac{1}{2}x-2 \end{gathered}[/tex]so, the slope of the line (1) = 1/2
the equation of the second line:
[tex]y=2x-2[/tex]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