The solid black graph in the image is $y = |x|$, which is a V-shaped graph centered at the origin. The dotted graph appears to be a transformation of $y = |x|$.

Let's analyze the transformations to determine which equation represents the dotted graph:

1. The dotted graph is a reflection of $y = |x|$ across the x-axis. Reflecting $y = |x|$ across the x-axis gives $y = -|x|$.

2. The dotted graph appears to be shifted downwards compared to $y = |x|$. This suggests that we need to subtract a value from $y = -|x|$.

3. From visual inspection, the dotted graph has been shifted 1 unit downwards. So, the equation of the dotted graph is $y = -|x| - 1$.

The correct answer is:

$y = -|x| - 1$.

Would you like a more detailed explanation or have any questions about graph transformations? Here are five related questions:

1. What are the basic transformations that can be applied to the absolute value function?
2. How do you identify horizontal and vertical shifts in a graph?
3. What is the effect of reflecting a function across the x-axis or y-axis?
4. How do you determine the vertex of an absolute value function?
5. How can you find the equation of a transformed graph given its visual representation?

Tip: When analyzing transformations, always start by identifying shifts, reflections, and stretches/compressions separately for clarity.