1. The problem asks what the graphs of the equations $x = a$ and $y = b$ represent. 2. The equation $x = a$ represents all points where the $x$-coordinate is constant at $a$, regardless of $y$. 3. Graphically, $x = a$ is a vertical line crossing the $x$-axis at $x = a$. 4. The equation $y = b$ represents all points where the $y$-coordinate is constant at $b$, regardless of $x$. 5. Graphically, $y = b$ is a horizontal line crossing the $y$-axis at $y = b$. 6. Therefore, $x = a$ is a vertical line and $y = b$ is a horizontal line. Final answer: The equations $x = a$ and $y = b$ represent vertical and horizontal lines, respectively.