Question

Equation of the line making intercepts $a$ and $b$ on $x$-and $y$-axis respectively is:

• A.
• B. y = ax + b
• C.
• D. ax + by = 0

Answer 1

Answer: (C)

Given:

The line makes the intercepts $a$ and $b$ on $x$-and $y$-axis respectively

i.e., the line passing through the points $(a,0)$ and $(0,b)$.

We know that, equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

$\Rightarrow$ Equation of the line passing through the points $(a,0)$ and $(0,b)$ is

$\frac{y-0}{b-0}=\frac{x-a}{0-a}$

$\Rightarrow \frac{y}{b}=-\frac{x-a}{a}$

$\Rightarrow ay=-bx+ab$

$\Rightarrow bx+ay=ab$

$\Rightarrow \frac{bx}{ab}+\frac{ay}{ab}=1$

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

Hence, option B is correct.