^ 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