7th Grade Math

PART

Get ConnectED

A BEC D

Variation

PART

Multi-Part

Lesson 3

GLE 0706.3.5

Understand and graph

proportional relationships.

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,

SPI 0706.3.4.

Lesson 3C Variation 405

Main Idea

Use direct variation to

solve problems.

Vocabulary

direct variation

constant of variation

slope-intercept form

y-intercept

Direct Variation

SPEED A car travels 130 miles in Speed of Car

200

100

0

300

150

50

250

350

123456789

(4, 260)

(3, 195)

Distance (mi) (2, 130)

Time (h)

2 hours, 195 miles in 3 hours, and

260 miles in 4 hours, as shown.

1. What is the constant rate of
   change, or slope, of the line?


2. Is the distance traveled always
   proportional to the driving time?
   What is the constant ratio?


3. Compare the constant rate of
   change to the constant ratio.

When two variable quantities have a constant ratio, their relationship

is called a direct variation. The constant ratio is called the constant of

variation.

Find a Constant Ratio

POOLS The height of the water as a pool is being filled is shown

in the graph. Determine the rate in inches per minute.

Since the graph of the data forms a line, the rate of change is

constant. Use the graph to find the constant ratio.

_heighttime _^2

5

or _0.4

1

_^4

10

or _0.4

1

_^6

15

or _0.4

1

_^8

20

or _0.4

1

The pool fills at a rate of 0.4 inch every minute.

a. SCUBA DIVING Two minutes after a diver enters the water, he has

descended 52 feet. After 5 minutes, he has descended 130 feet.

At what rate is the scuba diver descending?

V

d

Water in Pool

Height (in.)^2

0

4

510152025

6

8

Time (min)

(5, 2) (10, 4) (15, 6)

(20, 8)

404_415_C07_L3_895130.indd 405 12/31/09 4:32 PM