Problem 3 Diego made a graph of two quantities that he measured and said, "The points all lie on a line except one, which is a little bit above the line. This means that the quantities can't be proportional." Do you agree with Diego? Explain.

To analyze Diego's statement, we need to understand the concept of proportionality in the context of a linear relationship. 1. **Understanding Proportionality**: Two quantities are said to be proportional if they maintain a constant ratio. This means that if one quantity increases, the other quantity increases in a consistent manner, resulting in a straight line that passes through the origin (0,0) when graphed. 2. **Interpreting the Graph**: Diego mentions that "the points all lie on a line except one, which is a little bit above the line." This indicates that most of the data points follow a linear trend, suggesting a relationship between the two quantities. However, there is one point that deviates from this trend. 3. **Analyzing the Deviant Point**: The presence of a single point that is above the line does not necessarily mean that the two quantities cannot be proportional. It could indicate an outlier or an error in measurement. Proportionality is determined by the overall trend of the data points rather than the presence of a single outlier. 4. **Conclusion**: Therefore, I do not agree with Diego's conclusion that the quantities cannot be proportional based solely on the presence of one point above the line. The key factor is whether the majority of the points align with a linear relationship. If they do, the quantities can still be considered proportional, despite the outlier. In summary, the presence of one outlier does not invalidate the proportional relationship suggested by the other points.