The problem asks us to graph the equation $y = -\frac{1}{2}x + 3$ by creating a table of values and plotting the points without using slope and y-intercept shortcuts.

1. Problem Description

The problem asks us to graph the equation $y = -\frac{1}{2}x + 3$ by creating a table of values and plotting the points without using slope and y-intercept shortcuts.

2. Solution Steps

First, we will create a table of values for $x$ and $y$. Choose some convenient $x$ values, such as even numbers to avoid fractions, and calculate the corresponding $y$ values.

Let's choose the following x values: -4, -2, 0, 2,

4. Now we calculate the corresponding $y$ values using the equation $y = -\frac{1}{2}x + 3$.

- When $x = -4$: $y = -\frac{1}{2}(-4) + 3 = 2 + 3 = 5$

- When $x = -2$: $y = -\frac{1}{2}(-2) + 3 = 1 + 3 = 4$

- When $x = 0$: $y = -\frac{1}{2}(0) + 3 = 0 + 3 = 3$

- When $x = 2$: $y = -\frac{1}{2}(2) + 3 = -1 + 3 = 2$

- When $x = 4$: $y = -\frac{1}{2}(4) + 3 = -2 + 3 = 1$

Now we have the following pairs of points: (-4, 5), (-2, 4), (0, 3), (2, 2), (4, 1).

We will plot these points on the graph.

3. Final Answer

The graph of $y = -\frac{1}{2}x + 3$ is a line passing through the points (-4, 5), (-2, 4), (0, 3), (2, 2), and (4, 1).

```

Graph:

(x, y)

(-4, 5)

(-2, 4)

(0, 3)

(2, 2)

(4, 1)

The plotted points should be connected by a straight line.

```