Bell Work: Practice Set a – d on page 654−655.

Answer:  Yes  No  No  Yes

Lesson 99: Inverse Variation

In lesson 69 we studied direct variation in which the quotient of two variables is a constant. In most real-world applications, as one variable increases, the other increases. Direct Variation: y/x = k

In this lesson we will study inverse variation in which the product of two variables is a constant. In most real-world applications, as one variable increases, the other decreases. Inverse Variation: xy = k

Consider the following scenario: Every week Elizabeth bakes a loaf of cornbread for the family meal. The cornbread is a favorite – each person receives an equal portion, and it is always eaten completely. The size of each slice is small when many people are present but large when few are there.

The table shows the fraction of the cornbread each person receives, depending on the number of people present. Number of People Size of Slice 21/2 41/4 101/10

The relationship between serving size and the number of servings is an example of inverse variation, or inverse proportion. The product of the variables is constant. In this case, the constant is one loaf and the product of the variables (serving size and number of servings) is 1 for every number pair. As one variable changes, the other changes in such a way that their product is constant. An equation that describes the relation before is: n  s = 1 In this equation, n is the number of people present, s is the size of each slice, and 1 represents the whole loaf.

Example: Trinh travels 120 miles to visit his friend. If he averages 60 miles per hour, then the trip takes 2 hours.  What is the quantity that remains constant in this problem?  Fill in the chart with other possible rate and time combinations.  Show that the rates and times for Trinh’s trips are inversely proportional. Rate (mph)Time (hr)

Answer:  120 miles is the constant distance   Rate (mph)Time (hr)Rate x Time

Graph the points from the previous example.

This graph is characteristic of inverse variation. We see that the function is non-linear. Any variables x and y that are inversely proportional have a similar equation and graph.

Example: Robots are programmed to assemble widgets on an assembly line. the number of robots working (n) and the amount of time (t) it takes to assemble a fixed number of widgets are inversely proportional. If it takes 10 robots 8 hours to assemble a truckload of widgets, how long would it take 20 robots to assemble the same number of widgets?

Answer: 10  8 =  x = 80 x = 4 hours

HW: Lesson 99 #1-25