Lesson 5: Rate of Change and Slope

How is the "rate of change" in a table related to the "slope" of a line on a graph?

Why does a linear function have a constant rate of change while a nonlinear function does not?

In a real-world scenario, what does a slope of zero represent compared to an undefined slope?

Slope (m): The ratio of the vertical change (rise) to the horizontal change (run) between any two points on a line.
Rate of Change: A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.
Constant Rate of Change: The defining characteristic of a linear function where the ratio of change remains the same throughout.

8.F.B.4: 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.
8.F.A.2: Compare properties of two functions each represented in a different way (e.g., determine which function has a greater rate of change).

Description: This lesson teaches students the mechanics of calculating slope using the slope formula and "counting" rise over run on a coordinate plane. Students will apply this to tables to verify linearity.
Purpose: To quantify the "steepness" of functions. This is a prerequisite for writing full linear equations in the form y = mx + b DOK Level: Level 2 (Skill/Concept).

Run over Rise: Students frequently flip the slope formula
Subtraction Errors
Zero vs. Undefined: Students often confuse the slope of a horizontal line (0) with that of a vertical line (undefined).

Support: Use "Slope Triangles" on physical graphs so students can visually count the blocks for rise and run.
Scaffolding: Provide a "Slope Formula Organizer" where students can plug (x, y) coordinates into pre-drawn boxes to prevent subtraction errors.
Extension: Ask students to find the rate of change between two points on a nonlinear graph (like a parabola) to discover why it isn't "constant."

Exit Ticket