Algebra 1 Common Core Student Edition, Grade 8-9

Plan
How do you know
which x-values to
choose?
Choose positive and
negative values. Choose
x-values that divide
easily into 8 to get
ordered pairs that are
easy to graph.

You can graph an inverse variation xy = k or y = * by m aking a table of values an d

plotting points.

Graphing an Inverse Variation

What is the graph of y — *?

Step 1 Make a table of values.

&

D

-8 -4 -2 -1^01 2

4

. 8
-1 -2 -4 -8 undefined^8 421

W hen x = 0, there

is no y -va lu e.

Step 2 Plot the points from th e table. C onnect the points in

Q uadrant I w ith a sm o o th curve. Do th e sam e for the

points in Q u ad ran t III.

@ 3. a. W hat is th e graph of y = ^?

b.

How are they different?

b. Reasoning For k > 0, how are th e graphs of y = * an d y = — alike?k —k

I y

r5" 8

y =X

0 ti )X

s

\

1

Recall th at a direct variation is an equ atio n of th e form y = kx. The following summary

will help you recognize a n d use direct an d inverse variations.

Co n c ep t Su m m a r y Direct and Inverse Variations

Direct Variation

y

7

y = kx,k> 0

y varies directly with x.

y is directly proportional to y x.

The ratio * is constant.

In v e rs e V a ria tio n

r

y = !L ,k>0 y-f.K O

y varies inversely w ith x.

y is inversely p roportional to x.

The p ro d u c t xy is constant.

700 Chapter 11 Rat io nal Expressions and Funct ions