From Proportional to Linear: Graphs, Tables, and Equations
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Students will be able to determine whether a relationship is proportional or non-proportional, represent linear relationships using tables, graphs, and equations, and interpret slope and y-intercept in context.
Lesson Overview
Students progress from identifying proportional relationships through graphs and tables to writing and interpreting linear equations in slope-intercept form, distinguishing proportional from non-proportional linear relationships throughout.
Materials
- Vertical whiteboards or chart paper
- Dry-erase markers
- Random grouping tool
- Four-quadrant note sheet (printed)
- Mild/Medium/Spicy practice cards
Scaffolded Task Progression
[ Interactive graph / diagram, available in the full lesson ]
Runner A starts at the origin. Runner B starts 10 units ahead. Which runner shows a proportional relationship between time and distance? How do you know from the graph?
[ Interactive graph / diagram, available in the full lesson ]
For Runner A: make a table of values for . For Runner B: make a table of values for . Then compute the ratio for each runner at . What do you notice?
1. Write an equation for total cost in terms of hours .
2. Is this relationship proportional? Justify using the equation AND the graph.
[ Interactive graph / diagram, available in the full lesson ]
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