Let's solve the given problem step-by-step.

5.2.1: Completing the Table

The formula given is: $y = -x - 4$

We need to compute the output values for each input value:

1. For $x = -5$: $y = -(-5) - 4 = 5 - 4 = 1$ The ordered pair is: $(-5, 1)$.

2. For $x = -4$: $y = -(-4) - 4 = 4 - 4 = 0$ The ordered pair is: $(-4, 0)$.

3. For $x = 0$: $y = -(0) - 4 = -4$ The ordered pair is: $(0, -4)$.

4. For $x = 2$: $y = -(2) - 4 = -2 - 4 = -6$ The ordered pair is: $(2, -6)$.

So, the completed table should look like this:

| Ordered pair | (-5, 1) | (-4, 0) | (0, -4) | (2, -6) |

5.2.2: Plotting the Points

To plot the points on the Cartesian plane:

• Mark the points $(-5, 1)$, $(-4, 0)$, $(0, -4)$, and $(2, -6)$.
• Draw a straight line through these points to represent the equation $y = -x - 4$.

5.2.3: Determining Linearity

Since the equation $y = -x - 4$ is of the form $y = mx + c$ (a linear equation), the graph will be a straight line.

5.2.4: Determining Increase or Decrease

The coefficient of $x$ in the equation $y = -x - 4$ is negative ($-1$), indicating that the graph is decreasing.

Summary of Answers

1. Completed Table: Filled in with the computed values above.
2. Graph: Straight line plotted with the points.
3. Linearity: The graph is linear (a straight line).
4. Increase or Decrease: The graph is decreasing.

Would you like more details on any step? Here are five questions related to this topic:

1. How do you determine if an equation is linear or non-linear?
2. What is the importance of the slope in a linear equation?
3. How does the y-intercept affect the graph of a linear equation?
4. Can a linear equation have a horizontal or vertical line as its graph?
5. What methods can be used to solve linear equations graphically?

Tip: When plotting points on a graph, always label each point clearly to avoid confusion and ensure accuracy!