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(1.1) Tables and Graphs of Linear

Equations

For 1 gallon of gasburned, 20 pounds of C0 2 are emitted; for 2gallons of gasolineburned, 40 pounds of

C0 2 are emitted; for 3gallons of gasolineburned, 60 pounds of C0 2 are emitted; and

so on.

Gallonsof gas

x 0 1

Poundsof CO 2 y 0 20

2 3 4 540 60 80 100

Exploration

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Gallonsof gas x 0 1 2 3 4 5Poundsof CO 2

y 0 20 40 60 80 100

L ooking for Patterns

1) Predict the next x- andy- values.

2) What pattern did youuse to predict the nextnumbers?

3) Graph the pointsrepresented by thetable. Can you drawone straight linethrough all of the

points?

6

120

L ooking for Patterns

0306090

120150180

1 2 3 4 5 6

Gallons of gas

P o u n

d s o

f C O 2

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x y

-2 4-1 9

0 14

1 19

x y

-1 -10 -3

1 -9

2 -27

x y

8 25 6

2 10

-1 14

x y

1 12 4

3 9

4 16

x y

10 -28 3

6 8

4 13

x y

-3 04 1

11 3

18 6

Table 1 Table 3Table 2

Table 4 Table 5 Table 6

4) For each table, findthe differences in

consecutive x-values and inconsecutive y-values. Whichtables have a

constant differencebetweenconsecutive x-values? Whichtables also have a

constant differencebetweenconsecutive y-values?

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x y

-2 4-1 9

0 14

1 19

x y

-1 -10 -3

1 -9

2 -27

x y

8 25 6

2 10

-1 14

x y

1 12 4

3 9

4 16

x y

10 -28 3

6 8

4 13

x y

-3 04 1

11 3

18 6

Table 1 Table 3Table 2

Table 4 Table 5 Table 6

4) All the tables have aconstant differencebetween consecutivex-values. Tables 1,3, and 5 haveconstant differencesbetween consecutivey-values.

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5 ) For each table, graphthe points represented.Which tables represent

points that can all fiton a straight line? Arethese tables the sametables you listed inStep 4?

Table 1

20

15

-10

-5

0

5

10

15

20

-3 -2 -1 0 1 2 3

Table 2

-30

-25

-20

-15

-10

-5

0

5

10

15

20

-3 -2 -1 0 1 2 3

Not aStraight

L ine

StraightL ine

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5 ) For each table, graphthe points represented.Which tables represent

points that can all fiton a straight line? Arethese tables the sametables you listed inStep 4?

Table 3

-5

0

5

10

15

20

-3 -1 1 3 5 7 9 11 13 1 5

Table 4

-5

-2

1

4

7

10

13

1

-1 0 1 2 3 4 5

Not aStraight

L ine

StraightL ine

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5 ) For each table, graphthe points represented.Which tables represent

points that can all fiton a straight line? Arethese tables the sametables you listed inStep 4?

able 5

5

0

5

10

15

0 2 4 10 12 1 4

able

5

3

1

1

3

5

9

5 0 5 10 15 20Not aStraight

L ine

StraightL ine

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5) Tables 1, 3, and 5 represented points that fiton a straight line. These are also the tableswith constant differences in both consecutive x-and y-values in Step 4.

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6) How can you determine if variables in

a table represent points that will all fiton one line?

If the differences between consecutivex-values and consecutive y-values areconstant, then the points will all fit onone line. T hat is, the variables are saidto be L inearly Related .