Question

Find the equation of the straight line passing through the point $(3,4)$ and has intercepts which are in the ratio $3:2$.

• A. $2x+3y-18=0$
• B. $2x-3y-18=0$
• C. $2x+3y+18=0$
• D. None of these

Answer 1

The correct option is A $2x+3y-18=0$

Given ratio of intercepts $a:b=3:2$

Let $x-intercept=a=3m$

$y-intercept=b=2m$

$\frac{x}{3m}+\frac{y}{2m}=1$ which is passing through $(3,4)$, we get

$\frac{3}{3m}+\frac{4}{2m}=1$

$\frac{1}{m}+\frac{2}{m}=1$

$\frac{3}{m}=1$

$m=3$

Therefore,

$x-intercept=a=3m=3\times 3=9$

$y-intercept=b=2m=2\times 3=6$

So, the equation is

$\frac{x}{9}+\frac{y}{6}=1$

$\frac{2x+3y}{18}=1$

$2x+3y=18$

$2x+3y-18=0$

Hence, this is the answer.