ANSWER:
Line a and line b are perpendicular
Line a and line c are parallel
Line b and line c are perpendidular
STEP-BY-STEP EXPLANATION:
We know when lines are parallel or perpendicular because of their slopes.
Two lines are parallel when their slopes are equal and they are perpendicular when their slopes are inverse.
We can easily determine the slope if we solve for y in each case, like this:
[tex]\begin{gathered} y=-\frac{1}{2}x+4 \\ m_1=-\frac{1}{2} \\ \\ -4x+2y=6 \\ 2y=4x+6 \\ y=2x+3 \\ m_2=2 \\ \\ 4y+2x=12 \\ 4y=-2x+12 \\ y=-\frac{1}{2}x+6 \\ m_3=-\frac{1}{2} \\ \\ -\frac{1}{2}\cdot2=-1 \end{gathered}[/tex]Therefore:
Line a and line b are perpendicular
Line a and line c are parallel
Line b and line c are perpendidular
