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Subject:   RE: slope of a line
Author: Steve
Date: Mar 31 2004
I think the easiest way to explain this to kids is more philosophical.  Tell
your students to imagine a line that goes through the origin and has an
incredibly small slope.  At the origin, the angle between this line and the
x-axis will be incredibly small as well.  Next, tell them to think about a new
line, that goes through the origin, and cuts this angle in half.  The new line
will thus have a smaller slope than the original, but the slope will not be
zero.  Now with the new line, cut its angle in half.  You can infinitely cut the
angles in half to create smaller and smaller non-zero slopes.  Therefore, the
answer to your question is that theoretically, it is impossible to find the
smallest slope of a line that is greater than zero.  Obviously the same could be
done with the y-axis.  I hope that helps.

On Mar 31, 2004, msbee wrote:

My grade 9 math students have presented me with a problem I
have not been able to solve to my satisfaction.

If you draw a line which goes through the point of origin
(0,0) and it has a positive slope, ie it slants up to the
right, as the line comes closer to being horizontal the
slope of the line decreases and as it gets closer to being
vertial the slope of the line increases.

My class wants to know what the smallest slope is before it
becomes 0 or horizontal and what is the largest slope before
it becomes vertical or undefined.

Can anyone help me?

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