Getting Started 
Misconception/Error The student does not understand the basic form of a linear function. 
Examples of Student Work at this Level The student:
 Attempts to write the function recursively.
 Calculates the slope or the yintercept but is unable to write the function.
 Attempts to provide a verbal description or a graph.
 Attempts to look for a pattern but cannot find one.

Questions Eliciting Thinking What is the basic form of a linear function?
Why is it important to calculate the slope when writing a linear function?
How did you find the yintercept? What is always true of the yintercept?
How can you use the slope and yintercept to write the equation? 
Instructional Implications Review the concept of a linear function in twovariables emphasizing slopeintercept form. Be sure the student understands the specific role of the slope and the yintercept in determining functional values. Assist the student in using the slope and yintercept to write the equation of the line in slopeintercept form. Ask the student to write the equation using function notation. Then ask the student to calculate f(x) for several values of x given in the table to demonstrate that the function is correctly written. Provide additional opportunities to write equations of lines given two points on the line.
If needed, review function notation and guide the student to use function notation when writing equations of lines. Provide frequent opportunities to use function notation, so the student can become familiar and comfortable with its use. 
Moving Forward 
Misconception/Error The student has some understanding of the form of a linear function but is unable to complete writing the function. 
Examples of Student Work at this Level The student correctly writes the basic form of a linear function (e.g., y = mx + b) on his or her paper but is unable to correctly calculate either the slope or the yintercept or does not substitute either into the equation correctly.

Questions Eliciting Thinking What is the basic form of a linear function? What does m represent? What does b represent?
Can you explain why you wrote your function this way?
Did you check if the ordered pairs in the table satisfy your equation? 
Instructional Implications Be sure the student understands the role of the slope and yintercept in writing the equation of a line in slopeintercept form. Assist the student in using the slope and yintercept to write the equation of the line in slopeintercept form. Ask the student to write the equation using function notation. Then ask the student to calculate f(x) for several values of x given in the table to demonstrate that the function is correctly written.
If needed, review how to calculate the slope of a line given two points on a line. Assist the student in correctly setting up the slope calculation to avoid sign errors or the calculation of the reciprocal value. Review the concept of the yintercept. Be sure the student understands its basic form, i.e., (0, b), and how to recognize it in a table of values.
If needed, ask the student to graph the values from the table and to use the graph to identify the yintercept. Guide the student to then locate the yintercept in the table. Next, assist the student in using the graph to determine the slope. Relate this strategy to finding the slope using two ordered pairs from the table. Provide the student with additional opportunities to identify the yintercept and slope without graphing.
If needed, review function notation and guide the student to use function notation when writing equations of lines. Provide frequent opportunities to use function notation, so the student can become familiar and comfortable with its use. 
Almost There 
Misconception/Error The student makes a calculation or other minor error. 
Examples of Student Work at this Level The student:
 Makes a calculation error when calculating the slope.
 Neglects to use function notation or uses it incorrectly.

Questions Eliciting Thinking Can you check your slope calculation again? Did you compute the slope correctly?
What is function notation? What does it look like? How can it be used to write this function? 
Instructional Implications Assist the student in identifying and correcting any calculation errors. Correct any errors with the use of function notation. Explain to the student that even though y = 6x + 2 correctly describes the relationship between the independent and dependent variable, function notation should be used when writing the equation since it was used in the description of the problem and in the table. Provide frequent opportunities to use function notation, so the student can become familiar and comfortable with its use.
Consider using the MFAS tasks What Is the Function Rule? (FLE.1.2) and Functions From Graphs (FLE.1.2) if not used previously. 
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 correctly finds the slope and yintercept and writes the function as f(x) = 6x + 2.

Questions Eliciting Thinking How did you know that (0, 2) was the yintercept (if the student identifies the yintercept in the table)?
Is there an easier way to find the yintercept (if the student calculates the yintercept)?
Suppose the directions did not state that this function was linear, how could you determine that it is linear? 
Instructional Implications Ask the student to write linear functions given a verbal description or a graph of the function. Consider using the MFAS tasks The Cost of Water (FLE.1.2), What Is the Function Rule? (FLE.1.2), and Functions From Graphs (FLE.1.2) if not used previously. 