Determine which graph represents the following relationship:
The number of triangles is one-third the number of sides.
(1 point)
Responses
The graph of a line passes through the points (0, 0) and (3,1).
Image with alt text: The graph of a line passes through the points (0, 0) and (3,1).
The graph of a line passes through the points (0, 0) and (2,1).
Image with alt text: The graph of a line passes through the points (0, 0) and (2,1).
The graph of a line passes through the points (0, 1) and (3,2).
Image with alt text: The graph of a line passes through the points (0, 1) and (3,2).
The graph of a line passes through the points (0, 0) and (3, 4).
None of these graphs represent the relationship "The number of triangles is one-third the number of sides."
To determine which graph represents the relationship "The number of triangles is one-third the number of sides," we need to analyze the given options.
From the statement, we know that the number of triangles is one-third the number of sides. This implies that as the number of sides increases, the number of triangles also increases, but at a slower rate.
So, let's look at the options:
1. The graph of a line passes through the points (0, 0) and (3,1).
2. The graph of a line passes through the points (0, 0) and (2,1).
3. The graph of a line passes through the points (0, 1) and (3,2).
4. The graph of a line passes through the points (0, 0) and (3, 4).
We can rule out options 1, 2, and 3 because they don't represent a relationship where the number of triangles is proportional to the number of sides. These options depict linear relationships where the rate of change is constant.
Hence, the correct graph is option 4, where the line passes through the points (0, 0) and (3, 4). In this graph, the rate of change is not constant, and the number of triangles is one-third the number of sides.
To determine which graph represents the relationship "The number of triangles is one-third the number of sides," we can analyze the given options.
The relationship states that the number of triangles is one-third the number of sides. Let's break down this relationship:
1. If the number of triangles is one-third the number of sides, it means the number of triangles is some fraction (specifically one-third) of the number of sides.
2. A line graph can represent this relationship because it shows a direct proportionality between the number of sides and the number of triangles. The slope of the line represents the constant ratio between the two variables.
Now, let's examine the graphs to determine which one represents the given relationship:
1. The graph of a line passing through the points (0, 0) and (3, 1) does not represent the relationship described. The slope of this line is 1/3, which indicates that the number of triangles is one-third the number of sides. Thus, this graph represents the given relationship.
2. The graph of a line passing through the points (0, 0) and (2, 1) also does not represent the relationship. The slope of this line is 1/2, not 1/3.
3. The graph of a line passing through the points (0, 1) and (3, 2) represents a different relationship, not the one described. The slope of this line is 1/3, but the intercept is not at (0, 0).
4. The graph of a line passing through the points (0, 0) and (3, 4) does not represent the given relationship. The slope of this line is 4/3, which does not match the required slope of 1/3.
Therefore, the graph that represents the relationship "The number of triangles is one-third the number of sides" is the graph of a line passing through the points (0, 0) and (3, 1).