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Consider the set of all points \((x,y)\) in the coordinate plane for which one of the coordinates is exactly negative three times the other or positive three times the other. If we were to plot all such points, into how many regions would the resulting graph split up the plane?

 

My first guess was 4, but the program said that it was wrong, so I was confused. Help?

 Apr 1, 2020
 #1
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Notice that each unique case can be expressed as a line. For example, if the y-coordinate is three times the x-coordinate, then we can say that y=3x. Do you see how this can help?

 Apr 1, 2020
 #2
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Yep! I at first tried to use an equation but when I just graphed it out in my head, it became so obvious! :)

 Apr 1, 2020

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