Question

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)?

Answer 1

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.

`\begin{gathered} 3x+6y=12\:/3 \\ \\ x+2y=4 \\ \\ 2y=4-x \\ \\ y=-(x)/(2)+2 \end{gathered}`

2) And for the next one:

`\begin{gathered} y-4=-(1)/(2)(x+1) \\ \\ y=-(1)/(2)x-1+4 \\ \\ y=-(1)/(2)x+3 \\ \\ y=-(x)/(2)+3 \end{gathered}`

3) Note that the slope is -1/2 for both of those lines. That means we are dealing with two parallel lines.