Question
Which linear graph represents a proportional relationship?
a graph of a line that passes through the points 0 comma 2.5 and 1 comma 4
a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 1
a graph of a line that passes through the points 0 comma negative 3 and negative 1 comma negative 2
a graph of a line that passes through the points 0 comma 2.5 and 1 comma 4
a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 1
a graph of a line that passes through the points 0 comma negative 3 and negative 1 comma negative 2
Answers
GPT-4o mini
A proportional relationship is characterized by a linear graph that passes through the origin (0, 0). This means that there is a direct proportionality between the two variables, and the ratio of the two quantities remains constant.
Let's analyze the options given:
1. **A graph of a line that passes through the points (0, 2.5) and (1, 4)**: This line does not pass through the origin, so it does not represent a proportional relationship.
2. **A graph of a line that passes through the points (0, 0) and (4, -1)**: This line passes through the origin (0, 0), but it does not represent a proportional relationship because a proportional relationship requires that the line be straight and the other points must maintain a consistent ratio.
3. **A graph of a line that passes through the points (0, -1) and (1, -1)**: This line is horizontal and does not pass through the origin, so it does not represent a proportional relationship.
4. **A graph of a line that passes through the points (0, -3) and (-1, -2)**: This line also does not pass through the origin and thus does not represent a proportional relationship.
Based on this analysis, **none of the options** describe a linear graph that represents a proportional relationship. The correct characteristic of a proportional graph is that it passes through the origin (0, 0), and all provided options do not meet this criterion in a proportional manner.
Let's analyze the options given:
1. **A graph of a line that passes through the points (0, 2.5) and (1, 4)**: This line does not pass through the origin, so it does not represent a proportional relationship.
2. **A graph of a line that passes through the points (0, 0) and (4, -1)**: This line passes through the origin (0, 0), but it does not represent a proportional relationship because a proportional relationship requires that the line be straight and the other points must maintain a consistent ratio.
3. **A graph of a line that passes through the points (0, -1) and (1, -1)**: This line is horizontal and does not pass through the origin, so it does not represent a proportional relationship.
4. **A graph of a line that passes through the points (0, -3) and (-1, -2)**: This line also does not pass through the origin and thus does not represent a proportional relationship.
Based on this analysis, **none of the options** describe a linear graph that represents a proportional relationship. The correct characteristic of a proportional graph is that it passes through the origin (0, 0), and all provided options do not meet this criterion in a proportional manner.