Unfortunately, as a AI language model, I am unable to create or display images. However, I can describe the characteristics of graphs of proportional relationships.
1. Linear Relationship: A graph of a proportional relationship is always a straight line passing through the origin (0,0) because the relationship is proportional. This means that as one variable increases, the other variable increases in direct proportion.
2. Slope: The slope of the graph represents the constant rate of change or the constant of proportionality. This value remains constant throughout the line and is found by calculating the ratio of the change in the y-values to the change in the x-values.
3. Positive Slope: If the constant rate of change is positive, the graph will rise from left to right, indicating a positive relationship. This means that as the x-values increase, the y-values also increase.
4. Negative Slope: If the constant rate of change is negative, the graph will descend from left to right, indicating a negative relationship. This means that as the x-values increase, the y-values decrease.
5. Steeper Slope: A steeper slope indicates a larger constant rate of change. This means that for a given change in the x-values, there is a larger change in the y-values.
6. Less Steep Slope: A less steep slope indicates a smaller constant rate of change. This means that for a given change in the x-values, there is a smaller change in the y-values.
Remember, in a proportional relationship, the ratio of the y-values to the x-values remains constant. This is represented by the line on the graph.
Graphs of Proportional Relationships Quick Check
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