Getting Started 
Misconception/Error The student is unable to correctly identify or use the slope formula. 
Examples of Student Work at this Level The student does not correctly identify the slope formula or a technique for finding the slope. The student:
 Attempts to write the slope formula but provides an incomplete expression and is not sure what to do next.
 Does not provide the formula but attempts to calculate the slope using arbitrary numbers instead of variables or writes the equation of a specific line.
The student identifies the slope formula asÂ m= but:
 Does not substitute the coordinates of the two given ordered pairs, (0, 0) and (x, y).
 Substitutes incomplete or incorrect values for the variables.

Questions Eliciting Thinking What is the slope formula? How can you use the slope formula to find the slope of a line?
What do the variables in the slope formula represent?
What are the coordinates of the points you were given? Can you find the slope using these two points? 
Instructional Implications Review the concept of slope and how to find slope graphically, quantitatively (as a change in y over a corresponding change in x), and from an equation written in slopeintercept form. Describe slope as a rate of change (e.g., an amount of change in the dependent variable associated with a corresponding change in the independent variable). Review the slope formula, m= , and its relationship to the concept of slope. Make explicit the meaning of each variable in the slope formula as well as the meaning of and . Explain that determines the change in the yvalues of two points while determines the corresponding change in the xvalues. Guide the student to use the given points, (0, 0) and (x, y), to write an expression that represents the slope of the line and to write the equation of the line in slopeintercept form. Provide opportunities to calculate the slope of a line given two points on the line or given its graph. Include problems in which more than two points are given. Include lines with both positive and negative slope.
Consider administering the MFAS task Slope Triangles. 
Making Progress 
Misconception/Error The student does not understand what it means to write the equation of a line. 
Examples of Student Work at this Level The student identifies the slope formula and correctly substitutes the coordinates of the given points into the formula. However, the student is unable to transform the resulting equation into an equation of a line containing the point (0, 0). The student writes:
The student is unable to solve for y or does not recognize Â as an equation of a line. 
Questions Eliciting Thinking What does it mean to write an equation of a line? What might the equation of a line look like?
What is the difference between an equation and an expression? Did you write an equation or did you write an expression? 
Instructional Implications Review the concept of the equation of a line. Indicate that an equation can take many forms but includes an algebraic description of the relationship between the independent variable and dependent variable (or the x and ycoordinates of points on the line). Guide the student to transform his or her equation into an equation written in slopeintercept form. Explain that the equation y = mx describes, in general, the relationship between the independent variable and dependent variable ofÂ any line whose yintercept is (0, 0). Ask the student to use the general equation to write specific equations of lines given their slopes. 
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 substitutes the coordinates of the two given points into the slope formula getting m= Â and solves for y writing the equation asÂ y = mx.

Questions Eliciting Thinking If a line can Â be described by the equation y = mx, what information do you need to know about a specific line in order to write its equation?
If you know that a line passes through the origin, how can you use the coordinates of a point on the line, (x, y) to find the slope?
What would the equation of a line that crosses the yaxis at some point, b, look like, in slopeintercept form? 
Instructional Implications Ask the student to derive the equation of a line through the origin using a slightly different approach. Provide a figure of two similar triangles, one with vertices at (0, 0), (1, 0), and (1, m) and another with vertices at (0, 0), (x, 0), and (x, y). Ask the student to derive the equation of a line by writing a proportion of the ratios of height to base for the two similar triangles. For example, see the image below:
Challenge the student to derive the equation of a line with a yintercept of (0, b) with b 0. 