Linear Vertical Translation

① This GeoGebra example dynamically demonstrates the vertical translation of a linear function graph, showing how changing the constant term shifts the line up or down. ② The core mathematical concept is function graph transformation, specifically the effect of adding a constant k to a linear function f(x) to obtain g(x)=f(x)+k, and how this affects the y-coordinates of all points while preserving the slope. ③ Construction: Based on the summary, the objects include f (original linear function), k (translation amount), and g (translated function). By adjusting k via a slider or input, users can observe the vertical shift of the graph and compare corresponding points between f and g. ④ This is suitable for middle school or early high school students learning function transformations, as well as for teachers demonstrating the concept in class. It helps learners grasp that vertical translation does not alter the shape or slope of the line, only its position along the y-axis.