Formative Assessment 69

Assessment Problem: 

1. Graph y = 2x+1.  Explain your thinking as you create the graph.
2.  What would happen if you change the 1 to a 7?  What would happen to the graph? Why do you think that? 

3. Graph y = 2x+7.
4. Write the equation of a new line halfway between the lines you drew.

  •  Explain what it means for the new line to be half-way between the lines? 
  •  What should the slope of the new line be to lie between the two lines? 
  •  What should the y-intercept of the new line be to lie between the two lines? 
  •  What should the x-intercept of the new line be to lie between the two lines? 
  •  Graph the new line that is between the other two lines.
Common Responses: 

Students frequently associate changes in the value of “b” with horizontal shifts of linear functions rather than vertical shifts.

Mathematical Issues: 

These questions are aimed at uncovering how students think about how the value of “b” will affect the graph of a line. It is also aimed to uncover the relationship between the graphical representation of parallel lines and the algebraic representation of the slope of those lines. See also module Connecting graphs to algebraic relationships and entry The value of “b” in “y=mx+b.”

Domain: 
Analysis of Change
Theme: 
Linear functions
Common Core Standards: 
A-REI: Reasoning with Equations and Inequalities
Research References: 
Moschkovich, J. (n.d.). "Students" use of the x-intercept as an instance of a transitional conception. Educational Studies in Mathematics, 37(2), 169.