Analyze and solve pairs of simultaneous linear equations.
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the possible relationships of bivariate data. This module is important in setting a foundation for students’ work in algebra in Grade 9.
Topic A: Linear Functions (8.F.B.4, 8.F.B.5)
Lesson 1: Modeling Linear Relationships
Lesson 2: Interpreting Rate of Change and Initial Value
Lesson 3: Representations of a Line
Lessons 4–5: Increasing and Decreasing Functions
Topic B: Bivariate Numerical Data (8.SP.A.1, 8.SP.A.2)
Lesson 6: Scatter Plots
Lesson 7: Patterns in Scatter Plots
Lesson 8: Informally Fitting a Line
Lesson 9: Determining the Equation of a Line Fit to Data
Topic C: Linear and Nonlinear Models (8.SP.A.1, 8.SP.A.2, 8.SP.A.3)
Lesson 10: Linear Models
Lesson 11: Using Linear Models in a Data Context
Lesson 12: Nonlinear Models in a Data Context (Optional)
Topic D: Bivariate Categorical Data (8.SP.A.4)
Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table
Lesson 14: Association Between Categorical Variables