7th Grade Math

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PART ABCD E

Variation

Multi-Part

Lesson 3

SPI 0706.1.3

Recognize whether

information given in a table,

graph, or formula suggests a

directly proportional, linear,

inversely proportional, or

other nonlinear relationship.

Also addresses GLE 0706.1.5.

Main Idea

Graph inverse

variations.

Inverse Variation

Jackie rides her bike at an average rate of 4 miles per hour. This situation

can be represented by the direct variation equation d = 4 t, where d is the

distance in miles and t is the time in hours. The rate is a constant.

Suppose Jackie wants to bike 12 miles each day. Some days she rides

faster than others. This situation can be represented by the equation

12 = rt, where r is the rate.

Copy and complete the table for the equation 12 = rt.

t (hours) 12 8 6 ■■■■

r (miles per hour) 1 1.5 2 2.5 3 3.5 4

Copy and complete the graph of the ordered pairs from

Step 1. Connect the points with a smooth curve. The

first three points are done for you.

r

t

Miles per Hour

2

1

0

3

4

5

12345678910111213

Hours

Jackie’s Rate

the Results

1. Is the time proportional to the rate? Explain why or why not.


2. When the product of two variables is a constant, the relationship
   is an inverse variation. Which situation is an inverse variation:
   Jackie biking at 4 miles per hour or biking 12 miles at varying
   rates? Identify the constants in each situation.

Lesson 3D Variation 411

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