Question

Find the equation of the line passing through the point $(9,-1)$ and having its $x$-intercept thrice as its $y$-intercept.

• A. $x+3y-6=0$
• B. $x+3y+6=0$
• C. $x+3y-3=0$
• D. None of these

Answer 1

The correct option is A $x+3y-6=0$

Let ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ are $x$ and $y-intercepts$ respectively.

$x-intercept\left(a\right)=3(y-intercept)$

$a=3b$

The required line is passing through the point $(9,-1)$

$\frac{x}{a}+\frac{y}{b}=1$

$\frac{9}{3b}-\frac{1}{b}=1$

$\frac{9-3}{3b}=1$

$\frac{6}{3b}=1$

$\frac{2}{b}=1$

$b=2$

$y-intercept\left(b\right)=2$

$x-intercept\left(a\right)=3\times 2=6$

$\frac{x}{6}+\frac{y}{2}=1$

$\frac{x}{6}+\frac{3y}{6}=1$

$x+3y=6$

$x+3y-6=0$

Hence, this is the answer.