Rectangular coordinate system

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mcheytan

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Jan 25, 2008
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Can we decide if a line will pass through the top left (II) box in a coordinate system if we have a slope of -1/6????
Without using calculator or anything else?
 
Yes. With a negative slope, there is no deciding to it. It will make an appearance in Quadrant II and Quadrant IV.
 
I understand that a negative slope will make the line K go from right to left, but how do we know if it will pass through quadrant II when we do not even have a point of the line. It can pass through quadrants I and III without going into II or IV....I am just confused. because i know that the formula is y=mx+b, where m=-1/6,,,but we do not have x or y or b....
the line can pass anywhere in any of the quadrants and still have a slope of negative 1/6....
 
mcheytan said:
...how do we know if it will pass through quadrant II when we do not even have a point of the line.
Click to expand...
Draw a random line with a random negative slope. Look at the line. Think about the y-intercept.

Either the y-intercept will be at (0, b) for b > 0, or it won't.

Case 1 (b > 0): If the y-intercept is above the x-axis, will the line pass through the second quadrant? (Think about the line, for x < 0.) For x = 0, the line is above the x-axis. But will the line always remain above the x-axis? (Remember: This is a straight line, not a curvy one.) If the line goes below the x-axis at some point, for x > 0, then in what quadrant is the line?

Case 2 (b < 0): If the y-intercept is below the x-axis, then in what quadrant will the line be when x > 0? What about when x < 0? The y-intercept is below the x-axis for x = 0, but will the line forever stay below the axis? (Remember: This is a straight line, not a curvy one.) If the line goes above the x-axis at some point, for x < 0, then in what quadrant is the line?

A line with a negative slope might never enter the first or third quadrants, but what does the above investigation say about the second and fourth quadrants? :wink:

Eliz.
 
mcheytan said:
I understand that a negative slope will make the line K go from right to left
Click to expand...
What does that mean? Except for vertical lines, what line doesn't do this? Define "go from".
 
I knew that and you knew that, but nowhere is such a thing defined and nowhere did you state it clearly until I asked and you answered. You will do better in math if you stick with real definitions and get away from various forms of sloppy language.

Good work getting this idea. What's next?
 
Thanks 8-) sorry for the bad language heheheh I am learning!! I will get there eventually :idea:
 
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