smc

If a point is equidistant from the coordinate axes, then the absolute values of the x-coordinate and y-coordinate are equal. Since the point is on the line $3x+5y=15$, find the intersection point of $y=x$ and $3x+5y=15$ and the intersection point of $y=-x$ and $3x+5y=15$. Substituting $x$ for $y$ in $3x+5y=15$ results in $8x=15$, so $x=\frac{15}{8}$. That means $y=\frac{15}{8}$, so one of the points is in the first quadrant. Substituting $-x$ and $y$ in $3x+5y=15$ results in $-2x=15$, so $x=\frac{-15}{2}$. That means $y=\frac{15}{2}$, so the other point is in the second quadrant. Thus, the points are in quadrants $I$ and $II$, so the answer is $\boxed{\text{quadrants I, II only}}$.