This applet can model this situation: "A rectangle has a fixed area. If its length is 24 cm, it width is 7 cm. In general, the length is x cm and the width is y cm." Part 1: Move point [i]A[/i] and predict what will happen to point [i]B[/i]. When you move the point [i]A[/i] from the origin [i]O[/i] horizontally, you will notice that point [i]B[/i] moves from the origin [i]O[/i] vertically. We can use the letter [i]x[/i] to represent the independent variable which is the length of the horizontal line segment [i]OA[/i] (i.e., the distance point [i]A[/i] is from the origin). We can use the letter [i]y[/i] to represent the dependent variable which is the length of the vertical line segment [i]OB[/i] (i.e., the distance point [i]B[/i] is from the origin). Part 2: Turn "Show Point" on to reveal the position of point [i]C[/i]. Point [i]C[/i] is a way to represent both the [i]x[/i]-value and the [i]y[/i]-value simultaneously. That means that the point C shows a specific instance of the two related quantities. For example, when [i]x[/i] is 24, [i]y[/i] is 7. Part 3: Turn "Show Function" on to reveal the where all possible point [i]C [/i]can lie.
1. How many cm is the length if the width is 21 cm? 2. How are the two quantities [i]x[/i] and [i]y[/i] related? 3. What is invariant? (a) sum of the two quantities [i]x[/i] + [i]y[/i], (b) difference between the two quantities [i]x[/i] - [i]y[/i], (c) product of the two quantities [i]xy[/i], or (d) ratio of the two quantities [i]y[/i]/[i]x[/i]? Why?