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Question

Answers

(a) $\dfrac{3}{4}$,

(b) $\dfrac{4}{3}$,

(c) $-\dfrac{3}{4}$,

(d) $-\dfrac{4}{3}$,

(e) $-\dfrac{2}{3}$.

Answer
Verified

Given that the value of y-intercept of the line 4x – ay = 8 is thrice the value of its x-intercept. We need to find the value of ‘a’.

Let us draw the line showing its intercepts.

We know that the equation of the line showing x and y-intercepts are of the form $\dfrac{x}{a}+\dfrac{y}{b}=1$. Where x-intercept is a and y-intercept is b.

Let us convert the given equation of the line 4x – ay = 8 into the form that shows both x and y intercept.

We have the equation of the line as 4x – ay = 8.

$\Rightarrow \dfrac{4x-ay}{8}=\dfrac{8}{8}$.

$\Rightarrow \dfrac{x}{2}-\dfrac{ay}{8}=1$.

$\Rightarrow \dfrac{x}{2}+\dfrac{y}{\dfrac{-8}{a}}=1$.

$\Rightarrow \dfrac{-8}{a}$.

According to the problem it is given that y-intercept is 3 times the x-intercept.

$\Rightarrow \dfrac{-8}{a}=3\times 2$.

$\Rightarrow \dfrac{-8}{a}=6$.

$\Rightarrow \dfrac{-8}{6}=a$.

$\Rightarrow a=\dfrac{-4}{3}$.

We have found the value of ‘a’ as $\dfrac{-4}{3}$.

∴ The value of ‘a’ is $\dfrac{-4}{3}$.