To determine if two lines are intersecting or parallel, you need to examine their slopes and [katex] y- [/katex]intercepts. If the slopes of the two lines are different, the lines are intersecting. They will cross each other at a single point, which can be found by solving the system of equations formed by the two lines. If the slopes of the two lines are the same, but their [katex] y- [/katex]intercepts are different, the lines are parallel. They will never cross each other and will maintain the same distance between them. If the slopes of the two lines are the same and their [katex] y- [/katex]intercepts are also the same, the lines are coincident, meaning they are the same line. In this case, they will have infinitely many points in common. By analyzing the slopes and [katex] y- [/katex]intercepts of two lines, you can determine whether they are intersecting, parallel, or coincident.