Question

The equation of the following line in double intercept form, the $x-$ intercept and the $y-$ intercept are respectively.

$2x-y=3$

• A. $\frac{x}{\frac{3}{2}}+\frac{y}{3}=1,a=\frac{3}{2},b=3$
• B. $\frac{x}{\frac{3}{2}}+\frac{y}{-3}=1,a=\frac{3}{2},b=-3$
• C. $\frac{x}{\frac{2}{3}}+\frac{y}{-\frac{1}{3}}=1,a=\frac{2}{3},b=-\frac{1}{3}$
• D. $\frac{x}{\frac{2}{3}}-\frac{y}{\frac{1}{3}}=1,a=\frac{2}{3},b=\frac{1}{3}$

Answer 1

The correct option is B $\frac{x}{\frac{3}{2}}+\frac{y}{-3}=1,a=\frac{3}{2},b=-3$

The given equation of line: $2x-y=3$ ........ $\left(i\right)$

The equation of a line in two-intercept form is given by $\frac{x}{a}+\frac{y}{b}=1,$ ....... $\left(ii\right)$

where $a$ is $x-$intercept and $b$ is $y-$intercept.

To convert equation $\left(i\right)$ into two-intercept form, divide $\left(i\right)$ by $3$ we get

$\frac{2x}{3}-\frac{y}{3}=1$

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

Now compare it with $\left(ii\right)$ we get

$a=\frac{3}{2}$ and $b=-3$

Hence, option B is correct.