This applet can model this situation: "A candle is burning at a constant rate. It has burned 16 mm after 10 minutes. In general, the candle has burned y mm after x minutes." Part 1: Move point A and predict what will happen to point B 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 C Point C 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 x is 10, y is 16. Part 3: Turn "Show Function" on to reveal the where all possible point C can lie. To reset, click the circular arrows on the top-right corner of the GeoGebra-applet screen.
1. How are the two quantities [i]x[/i] and [i]y[/i] related? 2. 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]? How do you know?