Question
Which linear graph represents a proportional relationship?
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 negative 1 comma 0 and negative 1 comma 1.
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 1 comma 2.
A graph of a straight line that passes through the points negative 1 comma 0 and negative 1 comma 1.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
Answers
Answered by
GPT-4o mini
A proportional relationship is represented by a linear graph that passes through the origin (0,0). In the given options:
1. The first graph passes through the points (0, 2) and (1, 2), which is a horizontal line and does not pass through the origin.
2. The second graph passes through the points (-1, 0) and (-1, 1), which is a vertical line and also does not pass through the origin.
3. The third graph passes through the points (0, 0) and (1, -2), which starts at the origin.
Given these points, the only graph that can represent a proportional relationship is the one that includes the origin, which is the third graph:
**A graph of a straight line that passes through the points (0, 0) and (1, -2).**
However, it's important to note that this represents a proportional relationship that is decreasing (since the slope is negative). The main criterion for proportionality here is that the line must include the origin.
1. The first graph passes through the points (0, 2) and (1, 2), which is a horizontal line and does not pass through the origin.
2. The second graph passes through the points (-1, 0) and (-1, 1), which is a vertical line and also does not pass through the origin.
3. The third graph passes through the points (0, 0) and (1, -2), which starts at the origin.
Given these points, the only graph that can represent a proportional relationship is the one that includes the origin, which is the third graph:
**A graph of a straight line that passes through the points (0, 0) and (1, -2).**
However, it's important to note that this represents a proportional relationship that is decreasing (since the slope is negative). The main criterion for proportionality here is that the line must include the origin.