Getting Started 
Misconception/Error The student does not understand what it means to write a function. 
Examples of Student Work at this Level The student finds the slope (but writes it as rather than ) and is unable to continue.

Questions Eliciting Thinking Can you explain what you found?
What does it mean to write a function?
What do you know about functions? What kind of function is represented by this graph?
What information, other than the slope, do you need to write a linear function? 
Instructional Implications Review the concept of a function and what it means to write a function. Provide examples of functions and their graphs. Assist the student in developing an understanding of the onetoone relationship between solutions of an equation in two variables and points on its graph (AREI.4.10). Provide the student with an example of a linear function and its graph. Ask the student to identify the coordinates of a point on the graph and demonstrate how the coordinates satisfy the equation. Emphasize that the coordinates of every point on the graph satisfy the equation, and every solution of the equation is represented by a point on the graph.
Review the concept of a linear function in twovariables emphasizing slopeintercept form. Review the concept of the slope of a line and how to calculate it from a graph. Assist the student in correctly identifying and counting the rise and the run. Review the concept of the yintercept. Be sure the student understands its basic form [i.e., (0, b)] and how to recognize it on a graph. In addition, provide instruction on calculating the yintercept when its ycoordinate is not an integer. Provide additional examples of graphs of linear functions and ask the student to identify the slope and yintercept and then, write an equation in slopeintercept form.
Allow the student to use dynamic software, such as Math Open Reference, to explore slope (http://www.mathopenref.com/coordslope.html) and equations of lines (http://www.mathopenref.com/coordlineintro.html). Provide additional opportunities to write equations of lines given their graphs.
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.
Consider implementing MFAS task Graphing a Linear Function (FIF.3.7). 
Moving Forward 
Misconception/Error The student is unable to correctly calculate one or both parameters. 
Examples of Student Work at this Level The student understands what it means to write a linear function but:
 Makes errors in calculating both the slope and the yintercept.
 Correctly finds the slope of the graph, but estimates the yintercept rather than calculating it.

Questions Eliciting Thinking Can you explain how you found the slope and yintercept?
Can you find the actual yintercept without estimating or guessing? 
Instructional Implications Review the concept of slope of a line and how to calculate it from a graph. Assist the student in correctly identifying and counting the rise and the run. Review the concept of the yintercept. Be sure the student understands its basic form [i.e., (0, b)] and how to recognize it on a graph. In addition, provide instruction on calculating the yintercept when its ycoordinate is not an integer. Provide additional examples of graphs of linear functions and ask the student to identify the slope and yintercept and then, write an equation in slopeintercept form.
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.
Consider implementing MFAS task Writing a Function From Ordered Pairs (FLE.1.2). 
Almost There 
Misconception/Error The student makes a minor error in calculating a parameter or writing the function. 
Examples of Student Work at this Level The student:
 Determines the slope to be rather than . All other work is correct given this error.
 Makes a distributing error when calculating the yintercept.
 Correctly calculates the slope and yintercept but writes the equation as .

Questions Eliciting Thinking I think you made a slight error in calculating the slope (or in distributing ). Can you find it?
What does function notation look like? What is the difference between f and f(x)? 
Instructional Implications Provide specific feedback and allow the student to correct his or her error. Provide additional opportunities to write linear functions given their graphs.
Consider implementing other MFAS function writing tasks such as Writing a Function From Ordered Pairs (FLE.1.2), The Cost of Water (FLE.1.2), and What Is the Function Rule? (FLE.1.2). 
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 both the slope and yintercept and writes the function as . 
Questions Eliciting Thinking Can you explain how you found the slope? Could you have found the slope another way?
Can you explain how you found the yintercept? Could you have found the yintercept another way? 
Instructional Implications Ask the student to rewrite the equation in standard form (i.e., ax + by = c).
Challenge the student to write function rules for nonlinear functions. Consider implementing MFAS tasks Writing an Exponential Function From Its Graph (FLE.1.2), Writing an Exponential Function From Its Description (FLE.1.2), and Writing an Exponential Function From a Table (FLE.1.2).
Consider implementing other MFAS tasks such as Writing a Function From Ordered Pairs (FLE.1.2), The Cost of Water (FLE.1.2), and What Is the Function Rule? (FLE.1.2). 