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PPT – Patterns to Equations PowerPoint presentation | free to download - id: 26b338-ZDc1Z

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Patterns to Equations

Find the next three terms in the pattern

1, 4, 7, . . .

13,

16

10,

1, 4, 7,

Find the tenth termin the pattern

1,

4,

7,

10,

13,

16,

. . .

1st

2nd

3rd

4th

5th

6th

10th ?

The tenth term is...

28!

1,

7,

16,

19,

22,

4,

10,

13,

25,

Now find theone-hundredth term

1,

4,

7,

10,

13,

16,

. . .

1st

2nd

3rd

4th

5th

6th

100th ?

You dont really want to write out 100 terms, do

you?

1,

4,

7,

10,

13,

16,

. . .

1st

2nd

3rd

4th

5th

6th

100th ?

If so, go ahead andfind the 1,000th term.

1,

4,

7,

10,

13,

16,

. . .

1st

2nd

3rd

4th

5th

6th

1000th ?

If not, we need tofind a better way.

1,

4,

7,

10,

13,

16,

. . .

1st

2nd

3rd

4th

5th

6th

1000th ?

One way would be to write an equation which

calculates the y-value . . .

for any x-value.

The Pattern as Ordered Pairs.

x 1, y 1

x 2, y 4

x 3, y 7

1,

4,

7,

10,

13,

16,

. . .

1st

2nd

3rd

4th

5th

6th

1000th ?

Look for a pattern.

Put the x and y-values in a table and look for a

pattern...

Does the pattern workfor larger numbers?

As x increases by 1, y increases by 3.

As x increases by 3, y increases by 9.

Note The slope is the same between x 1 2,

between x 2 3, between x 3 6

So, if y mx b, and m (slope) 3, then

equation must be

To find b,

Take any known (x, y) pair, plug in the values

for x y and solve for b.

Solve

Now we can complete the equation.

What is the 100th term in the pattern?

Review the steps with a new example

Find the change in yover the change in x (slope).

1

1

-4

-4

Begin writing the equation,

Use one (x, y) pair from the table, substitute

and solve the equation for b.

Write the final equation with m and b.

m -4

b 14

Write the equation

1.

2.

3.

Answers

1.

2.

3.