Lesson: Graphing Lines

Comment on Graphing Lines

"The line is made of infinitely-many points" = mind blown!!!!!!
But then how can it be a line?
greenlight-admin's picture

It's a pretty esoteric concept, but one definition (from Wikipedia) says "a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation."

A line doesn't have infinitely many points if there's a clear-cut beginning and end to the line.
greenlight-admin's picture

I can see how you might believe that.
Let's examine the line segment that goes from 0 to 1 on the number line.
The point 1/2 (aka 0.5) lies on the line segment (since 0 < 0.5 < 1)
The point 1/3 (aka 0.333...) lies on the line segment (since 0 < 0.333... < 1)
The point 1/4 (aka 0.25) lies on the line segment (since 0 < 0.25 < 1)
The point 1/5 (aka 0.2) lies on the line segment (since 0 < 0.2 < 1)

So, any point in the form 1/k (where k is a positive integer) will lie on the line segment from 0 to 1 on the number line. Since there are infinitely-many positive integers, we can conclude that there are infinitely many points on a line segment with a clear-cut beginning and end.

in your explination while testing option 3 i.e(0,2)
here x=0 and y=2 then by mistake you had used 2 in place of x instead of 0 , while calculating the equation

case : (0,2)=
anyways it doesnt satisfy
greenlight-admin's picture

Good catch! I have edited my response.

Cheers and thanks,

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