The graph of a linear function is shown. 5 4 3 2 4 --5-4-3-2-1 1 -2 19 3 4 ? 2 3 4 5 X Which word describes the slope of the line? positive negative zero O undefined
The graph of a linear function is shown. 5 4 3 2 4 --5-4-3-2-1 1 -2 19 3 4 ? 2 3 4 5 X Which word describes the slope of the line? positive negative zero O undefined
Transcribed Image Text:### The Graph of a Linear Function
**Graph Explanation:**
The provided image shows a graph of a linear function represented on a Cartesian coordinate system. The x-axis (horizontal) and y-axis (vertical) are marked with values ranging from -5 to 5. The linear function is depicted as a horizontal line at y = -2, crossing the y-axis at -2.
**Question and Options:**
Adjacent to the graph, a question is posed: "Which word describes the slope of the line?"
The possible answers are provided as multiple-choice options:
- positive
- negative
- zero
- undefined
### Determining the Slope
In the given graph, the horizontal line remains constant at y = -2. This means there is no vertical change as the x-value changes. Therefore, the slope of this line is zero.
**Correct Answer:**
- zero
Transcribed Image Text:**Balloon Hat Creations: Analyzing the Graph**
A balloon artist creates balloon hats for children at a store’s grand opening. The graph below illustrates the relationship between the number of balloons remaining, denoted as \( y \), after creating \( x \) hats.
### Graph Description:
- **Title**: "Balloon Hat Creations"
- **X-Axis (Horizontal axis)**: Represents the number of hats created (\( x \)), ranging from 0 to 100.
- **Y-Axis (Vertical axis)**: Represents the number of balloons remaining (\( y \)), ranging from 0 to 500.
- The graph shows a straight line starting at the point (0, 500) and slanting downwards to about (90, 0).
The key features of the graph are:
1. **Linear Relationship**: The relationship between the number of created hats and the remaining balloons is linear.
2. **Negative Slope**: The line slopes downward from left to right, indicating that the number of remaining balloons decreases as the number of hats created increases.
### Question:
What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Select **three** options:
- [ ] positive slope
- [x] negative slope
- [x] constant slope
- [ ] increasing function
- [x] decreasing function
**Explanation**:
- **Negative Slope**: The line descends from left to right.
- **Constant Slope**: The rate of decrease (slope) is constant.
- **Decreasing Function**: The value of \( y \) decreases as \( x \) increases.
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![**Balloon Hat Creations: Analyzing the Graph**
A balloon artist creates balloon hats for children at a store’s grand opening. The graph below illustrates the relationship between the number of balloons remaining, denoted as \( y \), after creating \( x \) hats.
### Graph Description:
- **Title**: "Balloon Hat Creations"
- **X-Axis (Horizontal axis)**: Represents the number of hats created (\( x \)), ranging from 0 to 100.
- **Y-Axis (Vertical axis)**: Represents the number of balloons remaining (\( y \)), ranging from 0 to 500.
- The graph shows a straight line starting at the point (0, 500) and slanting downwards to about (90, 0).
The key features of the graph are:
1. **Linear Relationship**: The relationship between the number of created hats and the remaining balloons is linear.
2. **Negative Slope**: The line slopes downward from left to right, indicating that the number of remaining balloons decreases as the number of hats created increases.
### Question:
What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Select **three** options:
- [ ] positive slope
- [x] negative slope
- [x] constant slope
- [ ] increasing function
- [x] decreasing function
**Explanation**:
- **Negative Slope**: The line descends from left to right.
- **Constant Slope**: The rate of decrease (slope) is constant.
- **Decreasing Function**: The value of \( y \) decreases as \( x \) increases.](https://content.bartleby.com/qna-images/question/8013d441-5946-4d9d-b85b-992de95a8487/c1ad04b4-885f-4bd7-8981-a497463088a7/otjrupb_processed.png)
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