The image you provided contains a graph with two vectors labeled $y$ (in purple) and $z$ (in green). The task is to graph $y + z$ with its initial point at the initial point of $y$.

To explain the process:

1. Vector Addition: To find the sum of two vectors, $y + z$, you can perform the vector addition by placing the tail (starting point) of $z$ at the head (ending point) of $y$. This method is known as the "tip-to-tail" method.

2. Procedure:

   • First, identify the coordinates of the vectors $y$ and $z$. The initial point of $y$ is the origin (0, 0), and you can trace the direction and magnitude of $y$ and $z$ from the graph.
   • Now, for vector $y + z$, start at the initial point of $y$, and draw vector $z$ starting from the endpoint of $y$.
   • The vector $y + z$ will be the vector drawn from the origin (the initial point of $y$) to the endpoint of the vector $z$, as added to $y$.

Would you like me to walk through the detailed calculations or any specific part of the process? Let me know!

Further Questions:

1. What is the coordinate of the endpoint of vector $y$?
2. What is the coordinate of the endpoint of vector $z$?
3. Can you explain how to add vectors geometrically in 2D?
4. How does the parallelogram law of vector addition relate to this process?
5. How do you calculate the magnitude of a vector from its components?

Tip:

When adding vectors geometrically, make sure the vectors are drawn to scale for accuracy!