This applet allows students to see an inversely proportional relationship between two co-varying quantities. If the value of [i]x[/i] (represented by the length of the green horizonatal line segment [i]OA[/i]) increases, the value of [i]y[/i] (represented by the length of the red vertical line segment [i]OB[/i]) decreases proportionally. The area of the rectangle is initially set at 168. The slider is for changing the value of the area of the rectangle.
By turning on "Show Point", students can learn that the point [i]C[/i] at position ([i]x[/i],[i] y[/i]) means it is [i]x[/i] units away from the vertical axis and [i]y[/i] units away from the horizontal axis. A point ([i]x[/i], [i]y[/i]) shows one specific instance. With the "trace" function on, all possible points for C are plotted. This applet allows us to see the power of graphing on a Cartesian plane; a graph of points can capture dynamic co-varying information in a static 2-D representation.
By turning on "Show Function", the line representing the relationship between the two quantities [i]x[/i] and [i]y[/i] becomes visible. A function can also be represented by a set of instances such as (24, 7). Each instance can be represented using Cartesian coordinates. A graph is a set of points with [i]x[/i] and [i]y[/i] values that satisfy the equation for the function.
The big idea for this applet is that quantities whose product is invariant (i.e. xy = K where K is constant) are related by an inverse variation (i.e., y = K/x). We say that y is inversely proportional to x.
