To graph the equation $y = \frac{x}{2} + 1$, you need to plot several points and connect them with a straight line.

First, recognize that $y = \frac{x}{2} + 1$ represents a linear equation, which means its graph will form a straight line. This equation is structured in the slope-intercept form $y = mx + c$, where $m$ represents the slope (gradient) and $c$ is the y-intercept. In this case, we have $m = \frac{1}{2}$ and $c = 1$.

Begin by plotting the y-intercept. When $x = 0$, the value of $y$ is:

Thus, you should plot the point $(0, 1)$ on the graph.

Next, utilize the slope to find an additional point. The slope $\frac{1}{2}$ indicates that for every 2 units you move horizontally (to the right along the x-axis), you will move 1 unit vertically (upward along the y-axis). Starting from the point $(0, 1)$, move 2 units to the right to $x = 2$ and then 1 unit up to $y = 2$. This gives you the point $(2, 2)$, which you should also plot.

For accuracy, it is beneficial to plot a third point. For instance, when $x = -2$, you can calculate $y$ as follows:

Thus, you will plot the point $(-2, 0)$.

Now, draw a straight line through the points $(0, 1)$, $(2, 2)$, and $(-2, 0)$. Use a ruler to ensure that the line is straight. Extend the line in both directions and add arrows at each end to indicate that it continues infinitely.

Finally, label the axes and the line with its equation $y = \frac{x}{2} + 1$. This labeling will help anyone viewing the graph to understand its significance and the relationship it represents.