https://file.aiquickdraw.com/mathbot/file/172599465240466c55aof.jpg

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:

| Input values | -5 | -4 | 0  | 2  |
|--------------|----|----|----|----|
| Output values| 1  | 0  | -4 | -6 |

| 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!

The user is asked to complete a table for the linear equation y = -x - 4, plot the points on a graph, determine if the graph is linear or non-linear, and identify whether the graph is increasing or decreasing.

Learn how to solve the linear equation y = -x - 4 by completing the table of values, plotting points on a Cartesian plane, and determining the graph's characteristics. Suitable for Grade 9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation