Question
Which linear graph represents a proportional relationship?
Group of answer choices
A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.
Group of answer choices
A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.
Answers
GPT-4o mini
A proportional relationship can be identified by a straight line that passes through the origin (0,0). This means that for a relationship to be proportional, there should be a straight line that starts at the point (0,0) and maintains a constant ratio between the y and x values.
Let's analyze the given options:
1. **A graph of a straight line that passes through the points (0, 2) and (1, 2)**.
- This line is horizontal and does not pass through the origin. Hence, it's not a proportional relationship.
2. **A graph of a straight line that passes through the points (0, 0) and (1, -2)**.
- This line passes through the origin (0,0), which qualifies it as a proportional relationship, despite having a negative slope.
3. **A graph of a straight line that passes through the points (0, 2) and (2, 3)**.
- This line also does not pass through the origin as it intersects the y-axis at (0, 2). Thus, it does not represent a proportional relationship.
The correct answer is **A graph of a straight line that passes through the points (0, 0) and (1, -2)**, as it is the only one that represents a proportional relationship.
Let's analyze the given options:
1. **A graph of a straight line that passes through the points (0, 2) and (1, 2)**.
- This line is horizontal and does not pass through the origin. Hence, it's not a proportional relationship.
2. **A graph of a straight line that passes through the points (0, 0) and (1, -2)**.
- This line passes through the origin (0,0), which qualifies it as a proportional relationship, despite having a negative slope.
3. **A graph of a straight line that passes through the points (0, 2) and (2, 3)**.
- This line also does not pass through the origin as it intersects the y-axis at (0, 2). Thus, it does not represent a proportional relationship.
The correct answer is **A graph of a straight line that passes through the points (0, 0) and (1, -2)**, as it is the only one that represents a proportional relationship.