Question

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

$x+y=2$

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

Answer 1

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

The given equation is $x+y=2$ ....... $\left(i\right)$

An equation of any form can be expressed in double intercept form which is $\frac{x}{a}+\frac{y}{b}=1$, where $a$ and $b$ are $x$ and $y$ intercept respectively.

This can be done by the following steps

$\left(1\right)$ Given equation is in the form of $ax+by=c$

$\left(2\right)$ Divide both sides by $c$ and write the fraction $\frac{a}{c}$ and $\frac{b}{c}$ in the form $\frac{1}{\frac{c}{a}}$ and $\frac{1}{\frac{c}{b}}$

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

Hence, the $x$ - intercept = $2=a$ and $y$ -intercept = $2=b$