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Suppose the equation of the line is y = mx c where m is not zero.Then the x-intercept is (-c/m, 0) and the y-intercept is (0, c)

Therefore -c/m + c = k

multiplying by m, -c + cm = km

or c*(m -1) = km

and so, provided (m - 1) is not 0, c = km/(m - 1)

and the equations of the line are y = mx + km/(m - 1) for different values of m.


When m - 1 = 0, then m = 1 and so the equations are y = x + c so that the intercepts are (-c, 0) and (0, c) and so 2*c = k so the equation is y = x + k/2



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10y ago

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(xy'-y)(y'-1)+ky'=0

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Anonymous

4y ago
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Q: What is straight lines with algebraic sum of intercepts fixed as k?
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