Essential Questions:
How can I tell if an equation is linear from looking at its equation?
Big Idea:
Analyze linear and nonlinear equations in two variables, model with multiple representations.
Unit 4 instruction is focused on the following power standards:
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are linear.
8.F.A.4: 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.
Unit 4 instruction will be supported by the following standards:
8.EE.B.6: Use similar triangles to explain why the slope m is the same between an two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.EE.C.7: Solve linear equations in one variable.
8.F.A.1: 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.
8.F.A.5: 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.
How can I tell if an equation is linear from looking at its equation?
Big Idea:
Analyze linear and nonlinear equations in two variables, model with multiple representations.
Unit 4 instruction is focused on the following power standards:
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are linear.
8.F.A.4: 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.
Unit 4 instruction will be supported by the following standards:
8.EE.B.6: Use similar triangles to explain why the slope m is the same between an two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.EE.C.7: Solve linear equations in one variable.
8.F.A.1: 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.
8.F.A.5: 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.
What to TeachPrerequisite Skills from 7th Grade

Lesson Ideas 
Student PracticeIXL.com

Topic 1: Proportional Relationships

Topic 2: Working with Functions from Tables

Topic 3: Working with Functions from Equations

Topic 4: Working with Functions from Graphs

Topic 5: Comparing Functions

vocabularyfunction
function notation increasing at a constant rate decreasing at a constant rate positive slope negative slope linear nonlinear input output yintercept initial value rate of change xintercept horizontial veritcal parallel perpendicular sets ordered pairs tables coordinates rise over run slope origin xaxis yaxis undefined slope intercept form standard form independent variable dependent variable graph equation interpret AssessmentPre Assessment
Real World Experience Post Assessment Formative Assessment 
Unit Resources 
Learn the MathParent Letter 