Getting Started 
Misconception/Error The student is unable to describe any defining properties of linear functions. 
Examples of Student Work at this Level The student:
 Lists properties of operations.
 Attempts to define a function, referencing the vertical line test or single yvalues for each xvalue.
 States that a line is straight and/or goes on forever.
 Says it can be solved or that it has variables by themselves.

Questions Eliciting Thinking That’s a good definition for a function but what about a linear function? What makes a function linear?
What is the relationship between a line and a linear function?
What did you mean by ''solve a function''? Can only linear functions be solved? 
Instructional Implications Review the concept of a function emphasizing that a function is a relation in which each input value is paired with one output value. Provide examples of both functions and relations that are not functions described in a variety of ways (tables of values, mapping diagrams, algebraic rules, graphs, and verbal descriptions). Be sure to include many nonlinear examples of functions. Guide the student to carefully consider each example to determine whether or not it represents a function. Model explaining and justifying the reasoning behind the determination.
Review the concept of a linear function. Describe the equation of a linear function as one that can be written in the form ax + by = c (where b 0) but explain that linear functions may be written in other forms, some of which are quite useful (such as slopeintercept form). Explain to the student that a distinguishing feature of a linear function in two variables is that the variables are both raised to the first power. Provide many examples of equations of functions and ask the student to identify those that are linear. Then have the student justify his or her choices by writing the equations in the form ax + by = c. Next, focus on the slopeintercept form of the equation of a line. Provide examples of equations written in this form and ask the student to make a table of values for each equation. Then have the student use the table of values to graph each function. Use the graph as a means to explain the parameters of linear functions (e.g., constant rate of change or slope and initial value or yintercept). Guide the student to identify the slope and yintercept of an equation written in slopeintercept form and to use these parameters to graph the equation. Finally, provide examples of linear functions in context. Ask the student to find particular output values given their inputs and particular input values given their outputs. Challenge the student to explain the meaning of the intercepts and the slope in the context of the problem.
Be sure the student understands that the graph of a linear function is always a nonvertical line and every nonvertical line represents a linear function. Explain that a distinguishing feature of a linear function is that the rate of change is constant [e.g., any two values of x (or inputs) that differ by the same amount will have yvalues (or outputs) that differ by the same amount]. Illustrate this idea using tables of values and graphs.
Consider implementing other MFAS tasks for standard 8.F.1.3. 
Making Progress 
Misconception/Error The student describes nondefining properties as well as defining properties. 
Examples of Student Work at this Level The student describes one or some of the following properties of a linear function:
 Its graph is a nonvertical line.
 Its equation is of the form y = mx + b or ax + by = c.
 The two variables are each raised to the first power.
 The rate of change is constant.
In addition, the student describes a nondefining property such as:
 There are inputs and outputs.
 It will pass the vertical line test.
 The graph goes on forever.
 It has variables and constants.

Questions Eliciting Thinking Which of your properties are unique to linear functions? Do any of them apply to other functions as well?
Are all functions linear?
What makes a function linear? What distinguishes a linear function from all other types of functions? 
Instructional Implications Provide feedback to the student regarding both the correct and incorrect parts of his or her response. Explain the difference between properties of functions in general and properties unique to linear functions. Provide additional instruction on any defining properties the student did not list. Give the student opportunities to work with linear functions given in context. Ask the student to find particular output values given their inputs and particular input values given their outputs, graph the functions, and describe both the rate of change and initial value in context.
Consider implementing other MFAS tasks for standard 8.F.1.3. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student describes one or some of the following properties of a linear function:
 Its graph is a nonvertical line.
 Its equation is of the form y = mx + b or ax + by = c.
 The two variables are each raised to the first power.
 The rate of change is constant.

Questions Eliciting Thinking What does constant rate of change actually mean?
Is the equation of a linear function always in the form y = mx + b?
Is an equation of the form y = mx+ b always linear? Is its graph always a line? 
Instructional Implications Provide additional instruction on any defining properties the student did not list.
Expose the student to a variety of graphs to include linear, quadratic, cubic, rational, and exponential. Include both horizontal and vertical lines. Have the student indicate which graphs represent linear functions and why. Then give the student equations of various types of functions and have the student categorize the functions into linear and nonlinear. 