Question

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

Answer 1

lets say y intercept = c
so x intercept becomes : k-c

because their sum must equal to k.

got it so far ?

Answer 2

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

Answer 3

not exactly..

Answer 4

lets draw a picture

Answer 5

um, how is it?

Answer 6

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)

\[ y-y1 = \frac{y2-y1}{x2-x1}(x-x1)\]
\[ y-c = \frac{0-c}{k-c-0}(x-0)\]


\[ y-c = \frac{c}{c-k}(x)\]

Answer 7

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