Students construct linear functions to model real-world situations at a city sports and activity center. Using descriptions, tables, graphs, and data points, they identify rates of change and initial values, write equations in the form y = mx + b, and interpret slope and intercept in context. Aligned to CCSS 8.F.B.4 and ideal for practice or assessment.
Help students learn how to construct and interpret linear functions using realistic, connected scenarios from a city-run Sports and Activity Center. In this worksheet, students act as operations analysts, building linear models to represent costs, usage, and attendance across multiple center services.
This activity focuses on modeling from context, not just identifying equations, making it ideal for mastering CCSS 8.F.B.4.
A city operates a large Sports and Activity Center and tracks memberships, rentals, attendance, and resource usage using linear models. Different departments record data in descriptions, tables, graphs, and data points. Students analyze this information to build functions that help the city understand and predict costs and usage.
Across several connected scenarios, students will:
All problems fit within one consistent context:
Each scenario highlights a different way linear relationships appear in real life.
Aligned to CCSS: 8.F.B.4
Students will construct linear functions to model real-world relationships by determining the rate of change (slope) and initial value (y-intercept) from descriptions, tables, graphs, and data points. Students will write equations in the form y = mx + b and interpret the meaning of slope and intercept in context.
This worksheet supports randomization, meaning each student may receive different values, tables, graphs, or data points while practicing the same modeling skills. This promotes independent reasoning and reduces copying.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (*x, y*) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
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