SOLUTION: How do you identify whether the graph of a system of linear equations would be two intersecting lines, two distinct parallel lines, or two coincident lines?

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Question 577199: How do you identify whether the graph of a system of linear equations would be two intersecting lines, two distinct parallel lines, or two coincident lines?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
All you have to do is look at the slope.
If the equations are not already in this form:
+y+=+m%2Ax+%2B+b+, then put them into that form.
Look at +m+ for each equation.
+m+ is the slope of each.
Cases:
(1) +m+ is the same for all, but all the
+b+ 's are different
These are all parallel lines
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(2) +m+ is the same for all, and +b+
is the same for all.
These lines are coincident
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(3) +m+ is different for all the lines
( It doesn't matter what +b+ is )
All these lines intersect each other
None are coincident and
none are parallel
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