To intersect, their slopes have to be different. The y-intercept can be anything.
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NO they can't
No, vertical lines have an undefined slope.
The slope is the the same, Yet The y-intercept is not the same
For two dimensional lines: Get the formulas for the two lines into a format so that you can evaluate the slope. If the slopes are different, then they will intersect. If the slopes are the same, then you have two parallel lines, or possibly, the two equations describe the same line.
they are the same line.