Getting Started 
Misconception/Error The student is unable to interpret the constant term of a linear function either graphically or in context. 
Examples of Student Work at this Level The student incorrectly interprets the constant, 8, in the first equation. For example, the student says:
 The graph will be positive.
 Eight is the slope.
 Eight represents constant change.
The student may identify the constant in the equation L = 0.05W + 10 as 10 but is unable to explain its meaning in the context of the data.

Questions Eliciting Thinking Could you graph the equation y = 5x + 8? What will its graph look like? Would it cross the yaxis? If so, where?
What do you know about equations written in the form y = mx + b? What is m? What is b?
Do you know what constant term means?
When a linear equation is written in the form y = mx + b, what do the m and the b tell you about its graph? 
Instructional Implications Review the concepts of linear function, slope, and yintercept. Focus on the slopeintercept form of the equation of a linear function. Guide the student to carefully consider the context of the linear model given in this task, the specific variables the model relates, and how the variables are measured. Assist the student in graphing the linear model and in labeling and scaling the axes to fit the context. Relate the parameters in the equation to the slope of the graph and its yintercept. Then guide the student to explain the meaning of the constant term in the context of the data. Have the student initially identify the coordinates of the yintercept along with their units of measure [e.g., (0 pounds, 10 feet)]. Guide the student to relate the coordinates by saying, â€śWhen the weight is 0 pounds, the length is 10 feet.â€ť Ask the student to review the context of the data and to consider what it means for the weight on the bungee cord to be 0 pounds. Once the student understands that this will occur when there is no weight on the bungee cord, then ask the student to find the length of the bungee cord when the weight is zero. If necessary, have the student substitute zero for W and solve for L using the equation. Then show the student that this value of L is given in the equation. Be sure the student understands that this will only occur when the equation is written in slopeintercept form. Guide the student to conclude, â€śThe bungee cord is 10 feet long when there is no weight attached to it.â€ť
Provide additional examples of linear functions that have been fitted to data. Ask the student to identify the coordinates of the yintercept along with their units of measure. Encourage the student to describe the coordinates of the yintercept by associating the two values in a statement that explicitly includes what they represent along with their units of measure. Then remind the student to review the context of the data and to interpret the constant term in context. 
Moving Forward 
Misconception/Error The student can explain the significance of the constant term with regard to the graph of a linear function but is unable to explain its meaning in the context of data. 
Examples of Student Work at this Level The student says eight is the yintercept of the graph of the equation y = 5x + 8 or the point where the graph crosses the yaxis. The student is unable to correctly explain the meaning of 10 in the context of data modeled by the equation L = 0.05W + 10. The student says 10 is:
 The yintercept and offers no additional contextual explanation.
 The initial weight of the bungee cord.
 The rate of change.
 An amount that is added to 0.05w.

Questions Eliciting Thinking Can you write the yintercept of the equation L = 0.05W + 10 as an ordered pair? What does each coordinate represent in the context of this data? 
Instructional Implications Have the student initially identify the coordinates of the yintercept along with their units of measure [e.g., (0 pounds, 10 feet)]. Guide the student to relate the coordinates by saying, â€śWhen the weight is 0 pounds, the length is 10 feet.â€ť Ask the student to review the context of the data and to consider what it means for the weight on the bungee cord to be zero pounds. Once the student understands that this will occur when there is no weight on the bungee cord, ask the student, â€śWhat is the length of the bungee cord when the weight is zero?â€ť Guide the student to conclude, â€śThe bungee cord is 10 feet long when there is no weight attached to it.â€ť
Provide additional examples of linear functions that have been fitted to data. Ask the student to identify the coordinates of the yintercept along with their units of measure. Encourage the student to describe the coordinates of the yintercept by associating the two values in a statement that explicitly includes what they represent along with their units of measure. Then remind the student to review the context of the data and to interpret the constant term in context. 
Almost There 
Misconception/Error The student can describe the constant in terms of the variables in the context but is unable to fully interpret it. 
Examples of Student Work at this Level The student says eight is the yintercept of the graph of the equation y = 5x + 8. When interpreting the constant term of the equation L = 0.05W + 10, the student identifies 10 as a length but does not make explicit that the cord is 10 feet long when no weight is applied.

Questions Eliciting Thinking You said, â€śWhen the weight is zero, the length is 10 feet.â€ť When would the weight be zero? What does this tell you about the bungee cord?
What is the shortest length of the bungee cord that makes sense in this problem? When will the bungee cord be this length? 
Instructional Implications Ask the student to consider what it means for the weight on the bungee cord to be zero pounds. Once the student understands that this will occur when there is no weight on the bungee cord, then ask the student, â€śWhat is the length of the bungee cord when the weight is zero?â€ť Guide the student to conclude, â€śThe bungee cord is 10 feet long when there is no weight attached to it.â€ť
Provide additional examples of linear functions that have been fitted to data. Encourage the student to describe the coordinates of the yintercept by associating the two values in a statement that explicitly includes what they represent along with their units of measure. Then remind the student to review the context of the data and to interpret the constant term in context. 
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 says eight is the yintercept of the graph of the equation y = 5x + 8. When interpreting the constant term of the equation L = 0.05W + 10, the student explicitly relates a cord length of 10 feet to a weight of zero or no weight.

Questions Eliciting Thinking Could you find the greatest length the bungee cord could be?
Suppose you used this equation to determine the length of the cord when a 100 pound weight is attached. Would you expect the equation to predict the exact length? Why or why not? 
Instructional Implications Have the student determine and describe all possible values of LÂ (i.e., the range of the function L = 0.05W + 10).
Have the student consider how a linear function that has been fitted to data can be used to make predictions about values of variables. Guide the student to understand that predicted values may not be the same as actual values. Introduce the student to the concept of error in prediction and have the student calculate the predicted values and their residuals (i.e., the difference between the actual values and their predicted values) for a set of data modeled by a linear function. Provide a second model for the student to consider and have the student determine which model is best by comparing the sets of residuals. 