A ray travels along the line y = 2x - 5 and strikes the mirror x - 3y = 0…

Step 1. Where it strikes. $2x - 5 = \dfrac{x}{3}$ gives $x = 3$ and $y = 1$. The ray strikes at $(3, 1)$.

Step 2. Another point and its image. $(5, 5)$ is on the incident line. For the mirror $x - 3y = 0$, $t = \dfrac{5 - 15}{1 + 9} = -1$, so the image is $(5 + 2,\ 5 - 6) = (7, -1)$.

Step 3. The reflected line. It joins $(3, 1)$ to $(7, -1)$. The slope is $\dfrac{-1 - 1}{7 - 3} = -\dfrac{1}{2}$, so $y - 1 = -\dfrac{1}{2}(x - 3)$, which is $y = -\dfrac{x}{2} + 2.5$.

Step 4. Check. The mirror has slope $\dfrac{1}{3}$. The tangent of the angle between the mirror and the incident ray is $\dfrac{2 - 1/3}{1 + 2/3} = 1$. For the reflected ray it is $\left|\dfrac{-1/2 - 1/3}{1 - 1/6}\right| = 1$. The two angles are equal.