Question

Equation of a line which passes through the point $(-3,8)$ and cuts off positive intercepts on the axes whose sum is $7$ is

• A. $3x-4y=12$
• B. $4x+3y=12$
• C. $3x+4y=12$
• D. $4x-3y=12$

Answer 1

Answer: (B)

$4x+3y=12$

Let equation line is

$y=mx+c$

Thus $(-3,8)$ satisfies it

$\Rightarrow 8-3m+c\Rightarrow y=mx+8+3m$

Let $a$ & $b$ are its interceot thus

$a+b=7$

Put $y=0$

$\Rightarrow m(x+3)+8=0$

$\Rightarrow$ $b=x=\frac{-8-3m}{m}$

Put $x=0$

$\Rightarrow y=8+3m$

$\Rightarrow a=8+3m$

Since $a+b=7$

$\Rightarrow \frac{-8-3m}{m}+\frac{8+3m}{1}=7$

$\Rightarrow 3m^2+4m-6m-8=0$

$\Rightarrow m=2,-4/3$

$\Rightarrow y=2x+14$ or $y=\frac{-4}{3}+4$

$\Rightarrow 4x+3y=12$