Algebra 1 Common Core Student Edition, Grade 8-9

Inverse V a ria tio n

@ C om m on C ore State Standards

F-IF.B.5 Relate the domain o f a function to its graph

and, where applicable, to the quantitative relationship

describes... Also A-CED.A.2

MP 1, MP 2, M P 3 , M P 4

Objectives To w rite a n d g ra p h e q u a tio n s for in v erse v a ria tio n s

To com pare direct an d inverse variations

Getting Ready! <«► x C

Completing a small house ta k e s 1 person 168 days. You want to build a

house using few er th a n 15 w orkers and finish in few er th a n 14 days.

How many w orkers should you hire? For how many days? Explain.

More workers

need few er days.

Fewer workers

need m ore days.

siilflir

84 days

SSSR

#1*1

::s:!

I # | | # i

i • a s »

56 days 21 days

MATHEMATICAL

PRACTICES

Lesson ^

Vocabulary

in v erse v a r ia tio n

• c o n sta n t o f
  variation for an
  in verse variation

In th e Solve It, th e n u m b e r of construction days decreases as th e n u m b e r of workers

increases. The p ro d u ct of crew size an d construction days is constant.

Essential U nderstanding If the p ro d u ct of two variables is a n onzero constant,

th e n th e variables form an inverse variation.

Key Concept Inverse Variation

An equ atio n of th e form xy = k or y = where k + 0, is an inverse variation.

The constant of variation for an inverse variation is k, th e p ro d u ct x • y for an

o rdered p a ir (x, y) th a t satisfies th e inverse variation.

I:

Think

Make sure you don't

stop at 24 = k. To w rite

the inverse variation

equation, you have to

substitute 24 for k

in xy = k.

Problem 1 Writing an Equation Given a Point

Suppose y varies inversely with x, and y = 8 when x = 3. What is an equation

for the inverse variation?

xy=k Use the general form o f an inverse variation.

3(8) = k Substitute 3 forxand 8 fory.

24 = k Simplify.

xy = 2 4 W rite an equation. Substitute 24 for k in xy = k.

An eq u a tio n for th e inverse variation is xy = 24, or y = ir-

698 C h a p t e r 11 Rat io nal Expressions and Funct ions