The problem asks us to identify which of the given ordered pairs are solutions to the equation $y = -\frac{1}{2}x$ based on the graph provided.

1. Problem Description

The problem asks us to identify which of the given ordered pairs are solutions to the equation $y = -\frac{1}{2}x$ based on the graph provided.

2. Solution Steps

We need to check each ordered pair $(x, y)$ to see if it satisfies the equation $y = -\frac{1}{2}x$.

* $(-6, 3)$: Substitute $x = -6$ into the equation: $y = -\frac{1}{2}(-6) = 3$. Since the calculated $y$ value matches the given $y$ value, $(-6, 3)$ is a solution.

* $(-4, 2)$: Substitute $x = -4$ into the equation: $y = -\frac{1}{2}(-4) = 2$. Since the calculated $y$ value matches the given $y$ value, $(-4, 2)$ is a solution.

* $(-2, 1)$: Substitute $x = -2$ into the equation: $y = -\frac{1}{2}(-2) = 1$. Since the calculated $y$ value matches the given $y$ value, $(-2, 1)$ is a solution.

* $(0, 0)$: Substitute $x = 0$ into the equation: $y = -\frac{1}{2}(0) = 0$. Since the calculated $y$ value matches the given $y$ value, $(0, 0)$ is a solution.

* $(4, -2)$: Substitute $x = 4$ into the equation: $y = -\frac{1}{2}(4) = -2$. Since the calculated $y$ value matches the given $y$ value, $(4, -2)$ is a solution.

* $(8, -4)$: Substitute $x = 8$ into the equation: $y = -\frac{1}{2}(8) = -4$. Since the calculated $y$ value matches the given $y$ value, $(8, -4)$ is a solution.

3. Final Answer

(-6, 3), (-4, 2), (-2, 1), (0, 0), (4, -2), (8, -4)