1. INVERSE VARIATION Section 9.1

2. Solving Inverse Variation: Definition 1: A function in the form xy = k or y = k/x, where k ≠ 0, is an inverse variation. The constant of variation is k, the product x * y for an ordered pair (x, y).

3. Example 1: Writing an Equation Given a Point: a. Suppose y varies inversely with x and y = 7 when x = 5. Write an equation for the inverse variation. b. Suppose y varies inversely with x and y = 9 when x = 2. Write an equation for the inverse variation.

4. Example 2: Finding the Missing Coordinate: a) The points (3, 8) and (2, y) are two points on the graph of an inverse variation. Find the missing value. b) The points (3, y) and (5, 9) are two points on the graph of an inverse variation. Find the missing value.

5. TOTD Suppose y varies inversely with x, and a point on the graph of the equation is (8, 9). Write an equation for the inverse variation. The points (5, 6) and (3, y) are two points on the graph of an inverse variation. Find the missing value.

6. Example 3: Determining Direct or Inverse Variation: Do the data in each table represent a direct variation or an inverse variation? For each table, write an equation to model the data. xy 25 410 25

7. Example 3: Direct Variations and Tables: Do the data in each table represent a direct variation or an inverse variation? For each table, write an equation to model the data. xy 520 10 254

8. Example 4: Real-World Problem Solving: Explain whether each situation represents a direct variation or an inverse variation. a. Carpooling: The cost of $20 worth of gasoline is split among several people. b. School Supplies: You buy several markers for 70¢ each.

9. Example 5: Relating to the Real World Zoology: The heart rates and life spans of most mammals are inversely related. Write an equation to model this inverse variation. Use your equation to find the average life span of a cat (heart rate 126 beats/min). AnimalHeart rate (beats/min) Life Span (min) Mouse6341,576,800 Rabbit1586,307,200 Lion7613,140,000 Horse6315,768,000

10. Example 6: Continued A squirrel’s heart rate is 190 beats per minute. Find its average life span. An elephant’s life span is about 70 years. Find its average heart rate.

11. TOTD Explain whether each situation represents a direct variation or an inverse variation.  You buy several souvenirs for $10 each.  The cost of a $25 birthday present is split among several friends.