Tables and Patterns Leading to Linear Functions — lesson. Mathematics State Board, Class 7.

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Let's see how to create tables and how to write linear equations using two variables for patterns.

Look at the above pattern and form a table.

Let us take,

$x$ be the number of steps (or) number of columns and

$y$ be the number of square boxes within every column.

Number of steps $(x)$	$1$	$2$	$3$	$4$	…
Number of square boxes $(y)$	$2$	$4$	$6$	$8$	…

Now, find the relationship between the two variables

$x$ and

$y$ .

For

$x = 1$ ,

$y = 2$

$y$ can be rewritten as

$y = 2 \times 1$

$x = 1$ , we can write

$y = 2 \times x = 2x$ - - - - - - - (I)

For

$x = 2$ ,

$y = 4$

$y$ can be rewritten as

$y = 2 \times 2$

$x = 2$ , we can write

$y = 2 \times x = 2x$ - - - - - - - (II)

For

$x = 3$ ,

$y = 6$

$y$ can be rewritten as

$y = 2 \times 3$

$x = 3$ , we can write

$y = 2 \times x = 2x$ - - - - - - - (III)

For

$x = 4$ ,

$y = 2$

$y$ can be rewritten as

$y = 2 \times 4$

$x = 4$ , we can write

$y = 2 \times x = 2x$ - - - - - - - (IV)

From equation (I), (II), (III) and (IV):

We can generalise the relation as

$y = 2 \times x$ or

$y = 2x$ .

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2. Tables and Patterns Leading to Linear Functions

Theory: