functions
Grade 8 Module 4: Linear Equations
STANDARDS:
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
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, the function A = s2giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.
Construct a function to model a linear relationship between two quantities. 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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.
Topic A: Writing and Solving Linear Equations (8.EE.C.7)
Lesson 1: Writing Equations Using Symbols
Lesson 2: Linear and Nonlinear Expressions in
Lesson 3: Linear Equations in
Lesson 4: Solving a Linear Equation
Lesson 5: Writing and Solving Linear Equations
Lesson 6: Solutions of a Linear Equation
Lesson 7: Classification of Solutions
Lesson 8: Linear Equations in Disguise
Lesson 9: An Application of Linear Equations
Topic B: Linear Equations in Two Variables and Their Graphs (8.EE.B.5)
Lesson 10: A Critical Look at Proportional Relationships
Lesson 11: Constant Rate
Lesson 12: Linear Equations in Two Variables..
Lesson 13: The Graph of a Linear Equation in Two Variables
Lesson 14: The Graph of a Linear Equation―Horizontal and Vertical Lines
Topic C: Slope and Equations of Lines (8.EE.B.5, 8.EE.B.6)
Lesson 15: The Slope of a Non-Vertical Line
Lesson 16: The Computation of the Slope of a Non-Vertical Line
Lesson 17: The Line Joining Two Distinct Points of the Graph Has Slope
Lesson 18: There Is Only One Line Passing Through a Given Point with a Given Slope
Lesson 19: The Graph of a Linear Equation in Two Variables Is a Line
Lesson 20: Every Line Is a Graph of a Linear Equation
Lesson 21: Some Facts About Graphs of Linear Equations in Two Variables
Lesson 22: Constant Rates Revisited
Lesson 23: The Defining Equation of a Line
Topic D: Systems of Linear Equations and Their Solutions (8.EE.B.5, 8.EE.C.8)
Lesson 24: Introduction to Simultaneous Equations
Lesson 25: Geometric Interpretation of the Solutions of a Linear System
Lesson 26: Characterization of Parallel Lines
Lesson 27: Nature of Solutions of a System of Linear Equations
Lesson 28: Another Computational Method of Solving a Linear System
Lesson 29: Word Problems
Lesson 30: Conversion Between Celsius and Fahrenheit
Topic E: Pythagorean Theorem (8.EE.C.8, 8.G.B.7)
Lesson 31: System of Equations Leading to Pythagorean Triples