### 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 SlopeIn 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 **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.

Answered: Image /qna-images/answer/c1ad04b4-885f-4bd7-8981-a497463088a7.jpg

Answered: The graph of a linear function is…

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

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### 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

**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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