Algebra 1 Common Core Student Edition, Grade 8-9

Inductive reasoning is th e p ro c e s s o f r e a c h in g a c o n c lu s io n b a s e d o n a n o b s e r v e d

pattern. You can use inductive reasoning to predict values.

Should you connect
the points on the
graph w ith a solid
line?
No. The n u m b e r o f tile s
m ust be a w h o le number.
Use a d o tte d lin e to see
the trend.

Extending a Pattern

The table shows the relationship between the number

of blue tiles and the total number of tiles in each figure.

Extend the pattern. What is the total number of tiles in a

figure with 8 blue tiles?

Tiles

Method 1 D r a w a g ra p h.

Number of Tiles

72

w a 54

— 36 rs

+*o

Step 1 Graph the points. q

2 4 6

Blue Tiles

The to ta l num ber o f tiles is 72.

mmwmm

1 9

2 18

327

4 36

(^545)
f/ \
/
3
Step 2 The points fall on a
line. Extend the pattern
with a dashed line.
"T
Step 3 Find the point on the
line w ith x -c o o rd in a te 8.
The y-coordinate of
th is p o in t is 72.
Method 2 Write an equation.
y = 9x The to t a l n u m b e r o f tile s is 9 tim es th e num ber o f blue tiles.
= 9(8) Substitute 8 for x.
= 72 Simplify.
The total num ber o f tiles is 72.
Got It? 3. Use the tile figure from Problem 3.
a. M a k e a t a b le s h o w in g t h e n u m b e r o f o ra n g e t ile s a n d t h e t o t a l n u m b e r
o f t ile s i n e a c h fig u r e. H o w m a n y t ile s i n a ll w i l l b e i n a fig u r e w i t h 24
orange tiles?
b. M a k e a t a b le s h o w in g th e n u m b e r o f b lu e t ile s a n d t h e n u m b e r o f
y e llo w t ile s i n e a c h fig u r e. H o w m a n y y e llo w t ile s w i l l b e i n a f ig u r e w it h
24 b lu e tiles?
I
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