Graph the equation y = x and then change it to the equation y = x+3. Predict how the graph would change.
Many students respond that the graph would shift three units to the left, because we are adding 3 to the x-values.
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”.