First, given two equations, solve each one for y (in other words, get into y=mx+b form).
If m is different for the two equations, the two lines intersect at one point.
If m is the same for both equations but b (the y-intercept) is different, the lines are parallel. the slopes are the same, but the lines cut the y-axis at different points.
If both m and b are the same, the lines coincide. Slopes AND y-intercepts are the same.