Question

Suppose a line $L$ make $x$-intercept $a$ and $y$-intercept $b$ on the axes. Then, the equation of the line $L$ is

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

Answer 1

Answer: (A)

We know that $x$-intercept or $y$-intercept is distance at which line cut the $X$-axis or $Y$-axis respectively. Here, $x$-intercept is ' $a$ ' and $Y$-intercept is ' $b$ '.
Obviously L meets $X$-axis at the point $(a,0)$ and $Y$-axis at the point $(0,b)$
By two-point form of the equation of the line, we have
$y-0=\frac{b-0}{0-a}(x-a)$
or $ay=-bx+ab\text{, i.e., }\frac{x}{a}+\frac{y}{b}=1$

Thus, equation of the line making intercepts ' $a$ ' and ' $b$ ' on $X$-axis and $Y$-axis respectively, is $\frac{x}{a}+\frac{y}{b}=1$.