The given function is $y = 5|x|$, which represents a V-shaped graph due to the absolute value. The vertex of this function is at the origin, $(0, 0)$, since no horizontal or vertical shifts have been applied.

Steps to Graph:

1. Plot the Vertex: The vertex of $y = 5|x|$ is at $(0, 0)$. This is the starting point of the graph.

2. Plot Additional Points: The absolute value function produces two linear parts, one for $x \geq 0$ and one for $x < 0$. The slope for the positive part is 5, and the slope for the negative part is also 5.

3. Direction of the Graph: For $x > 0$, the graph follows $y = 5x$.
   For $x < 0$, the graph follows $y = 5(-x)$, which is equivalent to $y = -5x$.

4. Shape of the Graph: The result is a V-shaped graph with steep lines due to the coefficient 5.

Vertex:

You can click to plot the vertex at $(0, 0)$.

Would you like further details or to explore specific points on the graph?

Related Questions:

1. What would the graph look like if the function was $y = 5|x| + 3$?
2. How would changing the coefficient from 5 to 2 affect the graph?
3. How do you graph an absolute value function when it's shifted horizontally?
4. What is the difference in graphing $y = 5|x - 2|$ versus $y = 5|x + 2|$?
5. How does the slope of an absolute value graph affect its steepness?

Tip:

When graphing absolute value functions, the coefficient outside the absolute value affects the steepness of the lines, while constants inside the absolute value affect horizontal shifts.