How can we mathematically differentiate between a straight line and a curve?

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To differentiate between a straight line and a curve mathematically, it's essential to define both terms clearly. A straight line is characterized by a constant slope, while a curve has a variable slope that changes direction. The distinction can be formalized using calculus, where a straight line has a constant derivative, and a curve has a derivative that varies. Understanding these definitions is crucial for proving the differences between the two. Clear mathematical language and definitions are necessary for precise discussions on this topic.
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Homework Statement



How to prove line is a curve?

The Attempt at a Solution



I only know that line is a straight curve but how it can be proved?no idea!
Immediate help would be appreciated...:smile:
regards,
Momi
 
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Can you provide more context of the question and your "definitions" of "line" and "curve"?
Otherwise, the discussion isn't going to very precise... and you won't end up with a proof.
 
O didn't know that u could call a line for a curve, even a line segment would be a curve so it don't need to be continuous ..

http://en.wikipedia.org/wiki/Curve
 
I'm sure what you mean is that a curve and a straight line are different to you because, well, a straight line goes straight and a curve line changes directions. Put this into mathematical language!
 

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