Algebra 1 Common Core Student Edition, Grade 8-9

6 0U/fOf, ' j G etting Ready!

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Th e t ab le below shows t h e relat io nship b et ween t h e number o f kit es

in an arrangement and t he t o t al number o f ribbons on t he kit es' t ails.

Describe the pattern in the tab le. How many kites could you make

with 275 ribbons? Explain.

Patterns, Equations,

and Graphs

@ Common Core State Standards

A-REI.D.10 Understand that the graph o f an equation

in tw o variables is the set o f all its solutions plotted in

the coordinate plane, often forming a curve (which could

be a line). Also A-CED.A.2

MP 1, MP 2, MP 3, M P 4 , MP 7

Objective To use tables, equations, and graphs to describe relationships

One Kite Two Kites Three Kites Four Kites

5 R ib b o n s 10 R ib b o n s 15 R ib b o n s 2 0 R ib b o n s

Yo u can u se

patterns to make

predictions.

MATHEMATICAL

PRACTICES

Lesson
Vocabulary
so l u t i o n o f an
equat ion
inductive
reasoning

In the Solve It, you m ay have described the p a tte rn using w ords. You can also use an

e q u a t io n o r a g r a p h t o d e s c r ib e a p a t t e r n.

Esse n t i a l U n d e r st a n d i n g S o m e tim e s t h e v a lu e o f o n e q u a n t i t y c a n b e f o u n d

i f y o u k n o w th e v a lu e o f a n o th e r. Y o u c a n r e p r e s e n t th e r e la t io n s h ip b e t w e e n th e

q u a n t it ie s i n d if f e r e n t w a y s , in c lu d in g t a b le s , e q u a tio n s , a n d g ra p h s.

Y o u c a n u s e a n e q u a t io n w i t h t w o v a r ia b le s to r e p r e s e n t t h e r e la t io n s h ip b e tw e e n tw o

varying quantities. A solution of an equation w i t h t w o v a r ia b le s x a n d y is a n y o r d e r e d

pair (x, y) t h a t m a k e s t h e e q u a t io n tr u e.

Plan

How can you tell

whether an ordered

p a ir is a s o lu tio n?

Replace x with the first

value in the ordered pair

and y w ith the second

value in the ordered pair.

Is the resulting equation

true?

c

Id en tifyin g Solutions o f a T w o -V ariab le Equation

Is (3 ,1 0 ) a s o lu tio n o f th e e q u a tio n y = 4xl

y=4x

10 — 4 * 3 Substitute 3 for x and 10 fo r y.

10 12 So, (3 ,1 0 ) is n ot a solution o f y = 4x.

Got It? 1. Is th e o rd e re d p a ir a s o lu tio n o f th e e q u a tio n y = 4x?

a. (5, 20) b. (-5 , -2 0 ) c. (-2 0 , - 5 )

PowerAlgebra.com

d. (1.5, 6 )

Lesso n 1-9 Pat t er n s, Eq u at i o n s, an d Gr ap h s

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