Question

The equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$ is

• A. $2x+3y=13$
• B. $x+y=5$
• C. $3x+2y=12$
• D. $y-x=1$

Answer 1

Answer: (B)

Equation of line in intercept form is
$\frac{x}{a}+\frac{y}{b}=\mathrm{1.....}$(i)
Since, the line makes equal intercepts on the axes i.e.,
$a=b$
$\therefore$ From Eq. (i), $\frac{x}{a}+\frac{y}{a}=1$
$\Rightarrow x+y=a......$(ii)
Line (ii) passes through the point $(2,3)$, it will satisfy the line (ii).
$2+3=a\Rightarrow a=5$
Put the value of $a$ in Eq. (ii), we get
$x+y=5$