Please help Q5, Equation of all straight lines with algebraic sum of the intercepts fixed as k..

Question

ganeshie8 · Answer

lets say y intercept = c
so x intercept becomes :  k-c

because their sum must equal to k.

got it so far  ?

anonymous · Answer

so, y-(k-c)=mx+c? is this correct?

ganeshie8 · Answer

not exactly..

ganeshie8 · Answer

lets draw a picture

anonymous · Answer

um, how is it?

ganeshie8 · Answer

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ganeshie8 · Answer

u see, it goes through two points (0,c) and (k-c, 0)

now use the equation for a line going through two points (x1, y1) , (x2, y2)

$$ y-y1 = \frac{y2-y1}{x2-x1}(x-x1)$$
$$ y-c = \frac{0-c}{k-c-0}(x-0)$$


$$ y-c = \frac{c}{c-k}(x)$$

ganeshie8 · Answer

you can keep the equation as it is. it should be ok. or else you can try simplifying further..