Algebra 1 Common Core Student Edition, Grade 8-9

^ i Go t I t? 3. a. W eight on th e m o o n y varies directly w ith w eight on Earth x. A person

w ho w eighs 100 lb o n E arth weighs 16.6 lb o n th e m oon. W hat is an

eq u a tio n th at relates w eight o n E arth x a n d w eight on th e m o o n y? W hat

is th e graph of this equation?

b. Reasoning W hat is th e slope of th e graph of y = 0.38x in Problem 3?

How is th e slope related to th e equation?

Concep t Su m m ar y Graphs of Direct Variations

The graph of a direct variation eq u a tio n y = kx is

a line w ith the following properties.

• The line passes thro u g h (0, 0).


• The slope of the line is k.
  7

V.

k> 0

You can rew rite a direct variation eq u a tio n y = kx as * = k. W hen a set of data pairs

(x, y) vary directly, \ is th e co n stan t of variation. It is th e sam e for each d ata pair.

Plan
How can you check
your answer?
Graph the ordered pairs
in the coordinate plane.
If you can connect them
w ith a line th a t passes
through (0, 0), then y
varies directly w ith x.

Pr o b l em 4 Writing a Direct Variation From a Table

For the data in the table, does y vary directly with x? If it does, write an equation for

the direct variation.

Q

an

8 12

10 15

Find Vx for each ordered pair.

-= 1 5 —=15 4 8 1 3^1510 = 1.5

Find x for each o rdered pair.

3.2= -1.6? y = 2 A ^ = 0.4

The ratio * = 1-5 for each d ata pair.

So y varies directly w ith x. The direct

variation e q u a tio n is y = 1.5x.

y

The ratio * is n o t th e sam e for all data

pairs. So y does n o t vary directly

withx.

& G o t It? 4. For th e d ata in th e table at th e right, does y vary

directly w ith x? If it does, write an eq u a tio n for the

direct variation.

an

-3 1 2.25

1 -0 .7 5

4

c

PowerAlgebra.com Lesson 5-2 Direct Variation^303