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Hi, folks!
I need to check that given two lines both of whose slope is negative, then dividing one line by the other yields a third line whose slope is positive. I tried tinkering around with the algebra, but I can't seem to prove it.
Basically given two lines, y1 = m1x + c1, and y2 = m2x + c2, and given that m1 and m2 are both < 0, I thought it would be easy to show that if I divide the first line by the second, then the result would itself be a line whose slope is > 0.
But I can't seem to work it out.
I also tried selecting two points on both lines, via m = (y2 - y1)/(x2 - x1) and simply dividing the coordinates and then trying to create the line formula, but I can't separate the slope of the resulting equations into a form that depends only on x (it keeps getting mixed-up with y and the the c1, c2 constants).
Am I trying something that makes no sense?
Thanks,
Ed
I need to check that given two lines both of whose slope is negative, then dividing one line by the other yields a third line whose slope is positive. I tried tinkering around with the algebra, but I can't seem to prove it.
Basically given two lines, y1 = m1x + c1, and y2 = m2x + c2, and given that m1 and m2 are both < 0, I thought it would be easy to show that if I divide the first line by the second, then the result would itself be a line whose slope is > 0.
But I can't seem to work it out.
I also tried selecting two points on both lines, via m = (y2 - y1)/(x2 - x1) and simply dividing the coordinates and then trying to create the line formula, but I can't separate the slope of the resulting equations into a form that depends only on x (it keeps getting mixed-up with y and the the c1, c2 constants).
Am I trying something that makes no sense?
Thanks,
Ed