Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?

Parallel Lines.
1) T solve this question we need to work on these equations simplifying them as much as we can and then examining them.
[tex]\begin{gathered} 3x+6y=12\:\div3 \\ \\ x+2y=4 \\ \\ 2y=4-x \\ \\ y=-\frac{x}{2}+2 \end{gathered}[/tex]2) And for the next one:
[tex]\begin{gathered} y-4=-\frac{1}{2}(x+1) \\ \\ y=-\frac{1}{2}x-1+4 \\ \\ y=-\frac{1}{2}x+3 \\ \\ y=-\frac{x}{2}+3 \end{gathered}[/tex]3) Note that the slope is -1/2 for both of those lines. That means we are dealing with two parallel lines.