Getting Started 
Misconception/Error The student cannot effectively describe the relationship between two linearly related quantities. 
Examples of Student Work at this Level The student:
 Describes a feature of the graph and explains:
 It is a straight line.
 It is decreasing.
 There is a constant rate of change.
 Describes the relationship between the variables as if reading the graph from right to left.

Questions Eliciting Thinking What two quantities are modeled by this graph?
Can you describe the relationship the graph is modeling?
What kind of function is this? What do you know about this type of function? 
Instructional Implications Review the concept of a linear function, providing examples that include both equations and graphs. Emphasize that the rate of change of linearly related quantities is constant. Model describing the relationship between two linearly related quantities. For example, explain that the volume of fuel is decreasing at a constant rate over time. Guide the student to consider the intercepts by asking the student to represent each as an ordered pair that includes units of measure [e.g., (0 hours, n gallons of fuel) and (h hours, 0 gallons of fuel)]. Then have the student consider the context of the graph and explain the meaning of each intercept (e.g., the yintercept indicates the volume of gas in the jet’s tank was initially n gallons and the xintercept indicates that there will be no gas left in the jet’s tank after h hours).
Provide additional examples of functions, both linear and nonlinear, in context; ask the student to analyze and describe the relationship between the quantities. Guide the student to address features of the graph such as intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; and rate of change. Assist the student in learning and using mathematical terminology to describe these features. 
Moving Forward 
Misconception/Error The student does not describe the constant rate of change in the relationship. 
Examples of Student Work at this Level The student explains that as time increases, the fuel decreases but does not indicate that the decrease occurs at a constant rate.

Questions Eliciting Thinking What kind of function is this? What do you know about the rate of change of a linear function?
What does constant rate of change mean?
How much jet fuel is used each hour? Is it used up at a constant rate? 
Instructional Implications Review the concept of a linear function. Provide tables of values that represent linearly related quantities and show the student that linear functions grow by equal differences over equal intervals. Describe this rate of change as constant. Model describing the relationship between two linearly related quantities. For example, explain that the volume of fuel is decreasing at a constant rate over time.
Provide additional examples of functions, both linear and nonlinear, in context; ask the student to analyze and describe the relationship between the quantities. Guide the student to address features of the graph such as intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; and rate of change. Assist the student in learning and using mathematical terminology to describe these features. 
Almost There 
Misconception/Error The student does not provide a complete interpretation of the xintercept in context. 
Examples of Student Work at this Level The student explains that the volume of fuel is decreasing at a constant rate over time but when interpreting the xintercept, the student:
 Makes a statement about the graph.
 States the plane is out of fuel, but without regard to the variable time.

Questions Eliciting Thinking Can you reread the second question? How can you make your description more complete?
Can you identify the xintercept? What are the coordinates of this point? What do the coordinates represent? 
Instructional Implications Guide the student to consider the intercepts by asking the student to represent each as an ordered pair that includes units of measure [e.g., (0 hours, n gallons of fuel) and (h hours, 0 gallons of fuel)]. Then have the student consider the context of the graph and explain the meaning of each intercept (e.g., the yintercept indicates that initially the volume of gas in the jet’s tank was n gallons and the xintercept indicates that there will be no gas left in the jet’s tank after h hours).
Provide additional examples of functions, both linear and nonlinear, in context; ask the student to analyze and describe the relationship between the quantities. Guide the student to address features of the graph such as intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; and rate of change. Assist the student in learning and using mathematical terminology to describe these features. 
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 explains:
 The volume of fuel decreases at a steady or constant rate over time.
 The point where the graph intersected the xaxis would indicate the amount of time it takes for the jet to run out of fuel.

Questions Eliciting Thinking Would it make sense to extend this graph into another quadrant? Why or why not?
What feature of the graph corresponds to the rate of change? 
Instructional Implications Consider implementing MFAS Task Population Trend (8.F.2.5), which allows the student to investigate a nonlinear function and describe the relationship between the quantities. 