This section explores the relationship between the length and width of a rectangle with respect to the area.

Step 1: A rectangle has a width of 1 unit, length of 8 units and an area of 8 square units.

Step 2:

Step 3:

Step 4: Fill in the chart below.

Answer the questions and fill in the blanks below. Move your mouse over the blank to reveal the answer.

1. As you increased the width of the rectangle, what happened to the length of the rectangle?
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   Check Your Answer

   As the width of the rectangle increased, the length decreased.
2. Multiply the length and width of the rectangle. What do you observe?  What is another term for this?
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   Check Your Answer

   The product is constant, 8. This is also the area of the rectangle.
3. Use the STAT feature in your graphing calculator, plot the data where x is the width of the rectangle and y is the length of the rectangle.  Sketch the graph. Is this an inverse function?
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   Check Your Answer

   This is a graph of an inverse function where x > 0, the width increases as the length decreases.
   
4. Find an equation for the graph. 
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   Check Your Answer

   Since the value of k = 8 the equation of the graph is xy = 8 or 8 over x 8 x , where x is the width of the rectangle and y is the length of the rectangle.

Writing Activity on Inverse Variation

In your notes, write at least three things that you know about inverse variation, include information about tables, graph, equations, etc.