1. The problem asks to find the rate of change (slope) for the lines $x=5$ and $y=-2$. 2. The line $x=5$ is a vertical line where $x$ is always 5 regardless of $y$. 3. The line $y=-2$ is a horizontal line where $y$ is always -2 regardless of $x$. 4. The rate of change (slope) of a vertical line is undefined because the change in $x$ is zero, and slope is $\frac{\Delta y}{\Delta x}$. 5. The rate of change (slope) of a horizontal line is zero because the change in $y$ is zero. 6. Therefore, the rate of change for $y=-2$ is zero. Final answer: Rate of change for $y=-2$ is zero.