Getting Started 
Misconception/Error The student does not understand the slope criterion for parallel lines. 
Examples of Student Work at this Level The student is unable to find the slope of given the slope of the line to which it is parallel. 
Questions Eliciting Thinking What is the slope of a line whose equation is y = x + 10?
If parallel to this line, what is its slope?
Suppose line k is parallel to line j and that the slope of line j is 5. What is the slope of line k? 
Instructional Implications Remind the student that slope is a measure of a line’s “steepness.” Since two lines that are parallel are equally steep, suggest that it is reasonable that their slopes should be the same. To explore slopes of parallel lines, provide the student with the graphs of parallel lines and ask the student to use the graphs to calculate the slope of each line.
Guide the student through a proof of the criterion for parallel lines. 
Moving Forward 
Misconception/Error The student understands the slope criterion for parallel lines but cannot find the slope of a line given its equation in standard form. 
Examples of Student Work at this Level The student:
 Correctly identifies the slope of as but says that the slope of is 1 or 3.
 Indicates that he or she is unable to find the slope of the line given by the equation in Question 2.

Questions Eliciting Thinking How did you find the slope of ?
What form is the equation x + 3y =12 written in? Can you read the slope from this equation?
What could you do to find the slope of the line whose equation is x + 3y =12? 
Instructional Implications Review with the student the different forms of equations of lines. Provide the student with several equations written in each form. Have the student identify the equations written in slopeintercept form. Model rewriting equations in standard or pointslope form in slopeintercept form.
Provide the student with several examples of equations written in standard form or pointslope and ask the student to rewrite each equation in slopeintercept form and identify its slope as well as the slope of a line parallel to it. 
Making Progress 
Misconception/Error The student does not know to or is unable to algebraically find the yintercept of the line whose equation is to be written. 
Examples of Student Work at this Level The student can find the slope of the line whose equation he or she is writing but is unable to use a given point to write the equation. Instead, the student:
 Uses the yintercepts of the original equations as the yintercepts of the equations of the parallel lines.
 Uses the ycoordinate of the given point (2,7) as the yintercept of the equation of the parallel lines.
 Estimates the yintercept by graphing the line using the given point and the slope.

Questions Eliciting Thinking You said parallel lines have the same slope. Do parallel lines also have the same yintercept?
Why do you suppose you were told the coordinates of B? Is that needed to write the equation of ?
Is (2, 7) a yintercept? How can you tell if a point could be a yintercept?
What if the yintercept was a rational number such as 6.2? Do you think you could have found it by graphing? Do you know how to find it algebraically? 
Instructional Implications Have the student graph the line given by y= x+10 using its slope and yintercept. Then have the student graph the parallel line whose equation is to be written by using its slope, , and the given point, (2, 7). Have the student use the graph to estimate the yintercept of the parallel line. Then guide the student to find its actual value algebraically and to write its equation in slopeintercept form. Ask the student to repeat this exercise with the equation given in the second problem. When the student is finished, ask him or her if there was anything easier about writing the equation of the parallel line in the second problem.
Give the student more practice writing the equations of lines given points and equations of parallel lines written in a variety of forms. 
Almost There 
Misconception/Error The student makes a minor algebraic error. 
Examples of Student Work at this Level The student:
 Describes the slope of as x instead of .
 Leaves the equation in pointslope form instead of writing it in slopeintercept form.
 Substitutes the xcoordinate for the y value in the equation and the ycoordinate for the x value in the equation.

Questions Eliciting Thinking Is slope represented by a number or a term in an equation?
What form is your equation in? What form were you asked to write it in?
I think you made an error when you wrote this equation. Can you review your work and try to find the error? 
Instructional Implications Provide specific feedback to the student regarding his or her error and allow the student to revise the work on his or her paper. Give the student a few examples of common errors made when writing equations and have him or her identify and correct those errors. 
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 understands the slope criterion for parallel lines, correctly finds the slope of each line, and uses the given points to write the equations of the lines in slopeintercept form. The student provides the following answers:

Questions Eliciting Thinking What is the slope of a line perpendicular to y= x + 10?
What can you say about two lines that have the same slope and the same yintercept? 
Instructional Implications If you have not done so already, introduce the student to the slope criterion for perpendicular lines.
Ask the student to prove the slope criterion for parallel lines. Consider implementing MFAS task Proving the Slope Criterion for Parallel Lines (GGPE.2.5). 