Question

How to determine which two linear equations intersect?

Answer 1

Answer:

I understand that if the slopes are negative reciprocals then they will be perpendicular and intersect.

I also understand that if two lines have the same slope that the only way they can intersect is if they are on top of each. In this case, you would plug the coordinates into y = mx + b and if the equation checks out, then they intersect.

However, what if you have two line segments with different (not negative reciprocal) slopes?

Say for example line segment SR = S--> (5,2) and R --> (4,4) and line segment PQ = P--> (1,3) and Q--> (7,4)

My question boils down to what info do you need to know in order to determine whether two lines intersect?

I think this is very valuable info to know for the gmat.

Thanks!