Lesson objective: Understand that the slope of a linear graph tells us how the output value changes when the input value increases by one.

Students bring prior knowledge of rate of change from 8.F.B.4. This prior knowledge is extended to slope of linear graphs as students analyze a situation in which all information must be interpreted from a group of linear graphs. A conceptual challenge students may encounter is understanding the difference between positive and negative slopes, and realizing that this must be considered, and not just the steepness of a given line.

The concept is developed through work with graphs, which students must learn to interpret within a given context.

This work helps students deepen their understanding of number because it demonstrates that numbers do not simply represent quantities, but they can represent any number of things - in this case a relationship between two different quantities.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they analyze the arguments of the characters - specifically as they assess how the characters are interpreting the information provided by linear graphs.

**Key vocabulary:**

- initial value
- rate of change
- slope
*y*-intercept

**Special materials needed:**

- "Sample Investment Graphs" handout