1981 AHSME Problems/Problem 10

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If $(p, q)$ is a point on line $L$, then by symmetry $(q, p)$ must be a point on $K$. Therefore, the points on $K$ satisfy $x=ay+b$.Solving for $y$ yields $y = \dfrac xa-\dfrac ba$. $\Longrightarrow \boxed{E}$