Determine which graph represents the following relationship:
The number of triangles is one-third the number of sides.
The relationship described is that the number of triangles is one-third the number of sides. This means that for every 3 sides, there is one triangle.
Looking at the graphs:
- Graph A shows a linear relationship, where the number of triangles and sides increase proportionally. This is not the correct representation of the given relationship.
- Graph B shows a quadratic relationship, where the number of triangles increases at a faster rate than the number of sides. This is also not the correct representation.
- Graph C shows an inverse relationship, where as the number of sides increases, the number of triangles decreases. This is not the correct representation either.
- Graph D shows a relationship where the number of triangles increases at a slower rate than the number of sides. This is the correct representation of the given relationship.
To determine which graph represents the relationship "The number of triangles is one-third the number of sides," we need to understand how the number of triangles and sides are related.
Let's denote the number of triangles as T and the number of sides as S.
According to the given relationship, the equation can be written as:
T = (1/3)S
The equation states that the number of triangles (T) is equal to one-third (1/3) of the number of sides (S).
The graph representing this relationship will have the number of triangles (T) on the y-axis and the number of sides (S) on the x-axis.
Now, let's analyze the relationship further:
- If the number of sides is 3 (S = 3), then the number of triangles would be T = (1/3) * 3 = 1.
- If the number of sides is 6 (S = 6), then the number of triangles would be T = (1/3) * 6 = 2.
- If the number of sides is 9 (S = 9), then the number of triangles would be T = (1/3) * 9 = 3.
From these calculations, we can observe that as the number of sides increases, the number of triangles also increases, but in a proportionate manner.
Based on this relationship, the graph representing the relationship "The number of triangles is one-third the number of sides" should be a straight line passing through the origin (0,0) with a positive slope of 1/3.
Therefore, the correct graph would be a straight line with a positive slope passing through the origin, where every three units increase in the number of sides corresponds to a one-unit increase in the number of triangles.