Algebra 1 Common Core Student Edition, Grade 8-9

You can represent the same relationship between tw o variables in several

different ways.

Using a Table, an Equation, and a Graph

Ages Both Carrie and her sister Kim were born on October 25, but Kim was born

2 years before Carrie. How can you represent the relationship between Carrie's age

and Kim’s age in different ways?

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Kim w as born 2 years D iffe re n t w ays to rep re se n t Use a ta b le , an e q u a tion ,

before Carrie. th e re la tio n s h ip and a graph.

Step 1 M a k e a ta b le.

Carrie's and Kim's Ages (years)

Carrie's Age 1 2 3 45678910

Kim's Age 3 4 5 6 7 8 9 10 11 12

Think
Why does it make
sense to connect the
points on the graph?
A person's age can be
any p o s itiv e real number,
and th e ages o f th e girls
are always 2 years apart.
So eve ry p o in t o n th e
line makes sense in th is
situation.

S te p 2 Write an equation.

Let x = Carrie's age. Let y = K im 's age. F r o m t h e ta b le , y o u c a n see t h a t

y is a lw a y s 2 g r e a te r t h a n x.

So y = x + 2.

S te p 3 D r a w a g ra p h.

Carrie's and Kim's Ages

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Nj First, graph each

ordered pair

from the table.

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10

Carrie's Age (years)

2. aWill runs 6 la p s b e fo r e M e g a n j o in s h i m a t t h e tr a c k. T h e y t h e n r u n

to g e t h e r a t t h e s a m e p a c e. H o w c a n y o u r e p r e s e n t th e r e la t io n s h ip

b e tw e e n th e n u m b e r o f la p s W i l l r u n s a n d th e n u m b e r o f la p s M e g a n

runs in d iffe re n t ways? Use a table, an equation, and a graph,

b. Reasoning D e s c r ib e h o w t h e g r a p h i n P r o b le m 2 a b o v e w o u ld c h a n g e i f

th e d if f e r e n c e in ag e s w e r e 5 y e a rs in s te a d o f 2 y e a rs.

62 Ch ap t er 1 Fo u n d at i o n s f o r A l g e b r a