The equation $y = |x|$ represents a V-shaped graph that opens upwards, with the vertex (or the point of the "V") at the origin $(0, 0)$. Here's how you can visualize the graph:

1. Shape: The graph is composed of two straight lines.

   • The line $y = x$ for $x \geq 0$.
   • The line $y = -x$ for $x < 0$.

2. Vertex: The point where the two lines meet is called the vertex, and it is located at the origin $(0, 0)$.

3. Symmetry: The graph is symmetric with respect to the y-axis, meaning that for every point on the graph at $(x, y)$, there is a corresponding point at $(-x, y)$.

4. Slope:

   • For $x \geq 0$, the slope of the line is 1.
   • For $x < 0$, the slope of the line is -1.

5. Range: The range of the function is all non-negative real numbers, $y \geq 0$.

Would you like more details or have any specific questions? Here are some related questions to explore:

1. How does the graph of $y = |x|$ change if we add a constant, such as $y = |x| + 2$?
2. What happens to the graph of $y = |x|$ if we introduce a negative sign, like $y = -|x|$?
3. How can we describe the graph of $y = |x - 3|$?
4. What is the domain and range of the function $y = |x|$?
5. How does the graph of $y = |x|$ compare to $y = x^2$?

Tip: Understanding how absolute value functions transform will help you graph more complex functions involving absolute values easily!