To graph the function $y = |4x|$, we follow these steps:

1. Recognize the absolute value function: The equation $y = |4x|$ can be seen as a V-shaped graph. The key point here is the vertex of the graph, which is the point where the expression inside the absolute value equals zero.

2. Find the vertex: The vertex occurs when $4x = 0$. Solving this gives $x = 0$. Hence, the vertex is at the point $(0, 0)$.

3. Understand the slopes:

   • For $x \geq 0$, $y = 4x$ (the graph is linear and increases with a slope of 4).
   • For $x < 0$, $y = -4x$ (the graph is also linear but decreases with a slope of -4).

4. Plot key points:

   • $(0, 0)$ is the vertex.
   • For $x = 1$, $y = 4$, so point $(1, 4)$ is on the graph.
   • For $x = -1$, $y = 4$, so point $(-1, 4)$ is also on the graph.

I can plot this for you if you'd like. Would you prefer that?