Unit Plan 9 (Grade 8 Math): Lines in Slope–Intercept Form
8th graders derive and graph linear equations in slope–intercept form (y = mx + b) using similar triangles, interpreting slope (m) as rate of change and intercept (b) as starting value. Students connect equations to real-world contexts and distinguish linear from nonlinear relationships.
Focus: Derive y = mx + b from similar triangles and graph linear equations; interpret m and b in situations.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations • Functions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week students make the jump from “slope as rate” to full line equations in slope–intercept form. They will derive y = mx + b from slope and intercept ideas (using similar triangles), graph linear equations, and interpret m and b in real contexts. As an on-ramp to functions, students see y = mx + b as a rule that maps x to y and learn to spot when a relationship is not linear.
Essential Questions
- How do slope (m) and intercept (b) determine a line’s graph and story?
- Why does every non-vertical line have a constant slope, and how does that lead to y = mx + b?
- How can I tell when a relationship is linear vs nonlinear, and why does that matter?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Use similar triangles to explain constant slope and derive y = mx + b for a line with slope m and intercept b.
- Graph linear equations from y = mx + b and from two points or a point and slope; read m and b from graphs and tables.
- Interpret m and b in context (units, meaning of positive/negative, starting value vs rate).
- Recognize linear functions and give examples of nonlinear functions (intro to 8.F.3).
Standards Alignment — CCSS Grade 8
- 8.EE.6: Use similar triangles to explain why the slope m is the same between any two points on a non-vertical line; derive the equation y = mx + b for a line through (0, b) with slope m; give an equation for a line with a known slope and a point on the line.
- 8.F.3 (intro): Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear (for example, area of a circle with radius r is not linear in r).
Success Criteria (student-friendly)
- I can explain with a diagram why slope is constant and write y = mx + b.
- I can graph a line quickly using b (start) and m (rise/run).
- I can tell what m and b mean in a situation (for example, “$15 start-up fee and $2 per mile”).
- I can say whether a rule is linear or nonlinear and justify my decision.