Question

If $y$-intercept of the line $4x - ay = 8$ is thrice its $x$-intercept, then the value of a is equal to

• A. $\frac{4 }{3 }$
• B. $\frac{4 }{ 3}$
• C. -$\frac{ 3}{4 }$
• D. -$\frac{4 }{3 }$
• E. -$\frac{ 2}{ 3}$

Answer 1

Answer: (D)

Given, equation of line is
$4 x-a y=8 \,.....(i)$
We can write Eq. (i) in intercept from as,
$\frac{x}{2}+\frac{y}{-\left(\frac{8}{a}\right)}=1$
Here, $x$ - intercept $=2$
and $y$ - intercept $=-\frac{8}{a}$
According to question, $-\frac{8}{a}=3 \times 2 \Rightarrow -8=6 a$
$\Rightarrow a=\frac{-8}{6}=-\frac{4}{3}$