A point on the straight line, $3x+5y=15$ which is equidistant from the coordinate axes will lie only in

Given equation of line is $3x+5y=15..........\left(1\right)$

Clearly, a point of the line (1) which is equidistance from X and Y-axes will lie on the line either $y=x$ or $y=-x$

$\left.\begin{array}{r}y=x\\ 3x+5y=15\end{array}\right\}$ on solving $\left(\frac{{\displaystyle 15}}{{\displaystyle 8}},\frac{{\displaystyle 15}}{{\displaystyle 8}}\right)$

$\left.\begin{array}{r}y=-x\\ 3x+5y=15\end{array}\right\}$ on solving $\left(\frac{{\displaystyle -15}}{{\displaystyle 2}},\frac{{\displaystyle 15}}{{\displaystyle 2}}\right)$