Question

Find the equation of the straight line which passes through the point (-3, 8) and cuts off positive intercepts on the coordinate axes whose sum is 7.

Answer 1

$\text{Let equation of line be}\frac{x}{a}+\frac{y}{b}=1Thena+b=7anda\ge 0andb\ge 0\therefore \frac{x}{a}+\frac{y}{7-a}=1...\left(i\right)\text{The line passes through (-3, 8)}\Rightarrow \frac{-3}{a}+\frac{8}{7-a}=1\Rightarrow -21+3a+8a=7a-a^2\Rightarrow -2+11a=7a-a^2\Rightarrow a^2+4a-21=0\Rightarrow a=3or-7a\ne -7(asa\ge 0)\therefore a=3andb=4\therefore \text{Equation of line is}\frac{x}{3}+\frac{y}{4}=1or4x+3y=12$