Assessment Problem:

Graph the equation y = x and then change it to the equation y = x+3. Predict how the graph would change.

Common Responses:

Many students respond that the graph would shift three units to the left, because we are adding 3 to the x-values.

Mathematical Issues:

When beginning graphing, students have a tendency to believe that the “b” value in “y=mx+b” causes the graph to shift horizontally rather than vertically. This problem helps to uncover that thinking, and it helps students to see the relationship between changes in “b” and shifts in the x-intercept. See also Connecting graphs to algebraic relationships, and The value of “b” in “y=mx+b”.

Domain:

Analysis of Change

Theme:

Linear Functions

Common Core Standards:

7.EE: Expressions and Equations

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.