Section 9 1 INVERSE VARIATION Solving Inverse Variation

Section 9. 1 INVERSE VARIATION

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).

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.

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.

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.

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. x y 2 5 4 10 10 25

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. x y 5 20 10 10 25 4

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.

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). Animal Mouse Rabbit Lion Horse Heart rate Life Span (beats/min) (min) 634 1, 576, 800 158 6, 307, 200 76 13, 140, 000 63 15, 768, 000

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.

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.