Calculus/geometry

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Question
QUESTION: how many points are sufficient to draw a straight line

ANSWER: If you only had one point,
any other point would be on a line with it.  

If there were two points, we'll call them (x1,y1) and (x2,y2).

This is enough for a line, for the equation would be
y-y1 = m(x-x1) where m=(y2-y1)/(x2-x1).

Put in the values of the points and that's the equation for a line.


---------- FOLLOW-UP ----------

QUESTION: is one point sufficient to draw a straight line

Answer
No, since with only one point, it doesn't determine which way the line goes.  If you have a graph and know the point (1,1) is on the line, it could be any line of the form y-1 = m(x-1).  You could take m as 1, m as -1, m as 100, m as -2.456356, or whatever value is desired.  When (1,1) is put into the equation for x and y, the result is 0 = m*0, which is 0 = 0, which is always true no matter what value is chosen for m.

Calculus

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