Fifth graders studying linear functions would best represent the relationship between years and average income using which type of graph?

The appropriate choice for representing the relationship between years and average income is a scatterplot because it effectively displays how two variables relate to each other, especially when one variable is continuous, such as years, and the other, like average income, can also vary continuously.

In a scatterplot, individual data points are plotted on a Cartesian plane, allowing students to visually analyze trends, patterns, and correlations in the data. In the context of fifth graders studying linear functions, observing how average income changes with respect to the passage of time—years—is critical. This kind of visualization can help students understand concepts like positive and negative correlations and the overall trend of increase or decrease over time.

While a line graph can also show relationships over time, it is typically used when there is a continuous sequence of values, such as time intervals. A scatterplot, on the other hand, is more effective in showcasing individual data pairs and can clearly illustrate if there’s a linear relationship, which is fundamental to the study of linear functions.

Other graph types, like bar graphs and pie charts, are not suited for this type of data. Bar graphs usually represent categorical data, while pie charts show parts of a whole instead of relationships between two continuous variables. Thus, the use