WRITE THE FORMULA CONNECTING TWO VARIABLES X AND Y GIVEN IN THE TABLE

For each of the following tables, write a formula connecting the variables.

Check your formula for all the number pairs given :

Example 1 :

Solution :

Let the linear relationship between x and y is

y  =  Ax + B

(where x is input and y is output)

Here, input (x)  =  a

Output (y)  =  N

By writing the given values as ordered pairs, we get

(1, 4) (2, 6) (3, 8)(4, 10) (5, 12) (6, 14)

(1) – (2)

A + B – 2A – B  =  4 – 6

- A  =  - 2

A  =  2

By applying A  =  2 in equation (1), we get

2 + B  =  4

B  =  2

so, A  =  2 and B  =  2

By applying A  =  2 and B  =  2 in linear equation

N  =  2a + 2

Therefore, the formula is N  =  2a + 2

Example 2 :

Solution :

(1, 4) (2, 5) (3, 6) (4, 7) (5, 8) (6, 9)

 (1) – (2)

A + B – 2A – B  =  4 – 5

A  =  1

By applying A  =  1 in equation (1), we get

B  =  3

so, A  =  1 and B  =  3

By applying A  =  1 and B  =  3 in linear equation,

y  =  x + 3

Therefore, the formula is y  =  x + 3

Example 3 :

Solution :

y  =  Ax + B

7  =  A(1) + B

A + B  =  7 -----(1)

If 2^nd pair (2, 11)

y  =  Ax + B

11  =  A(2) + B

2A + B  =  11 -----(2)

Subtract (1) – (2), we get

A + B – 2A – B  =  7 – 11

A  =  4

By applying A  =  4 in equation (1), we get

4 + B  =  7

B  =  3

so, A  =  4 and B  =  3

By applying A  =  4 and B  =  3 in linear equation,

K  =  4c + 3

Therefore, the formula is K  =  4c + 3

Example 4 :

Solution :

(1, 4) (2, 11) (3, 18) (4, 25) (5, 32) (6, 39)

(1) – (2)

A + B – 2A – B  =  4 – 11

A  =  7

By applying A  =  7 in equation (1), we get

7 + B  =  4

B  =  - 3

so, A  =  7 and B  =  -3

By applying A  =  7 and B  =  -3 in linear equation,

Q  =  7d - 3

Therefore, the formula is Q  =  7d - 3

Example 5 :

Solution :

(1, 8) (2, 14) (3, 20) (4, 26) (5, 32) (6, 38)

(1) – (2)

A + B – 2A – B  =  8 – 14

A  =  6

By applying A  =  6 in equation (1), we get

6 + B  =  8

B  =  2

so, A  =  6 and B  =  2

By applying A  =  6 and B  =  2 in linear equation,

C  =  6h + 2

Therefore, the formula is C  =  6h + 2

Example 6  :

Solution :

(1) – (2)

A + B – 2A – B  =  6 – 14

A  =  8

By applying A  =  8 in equation (1), we get

8 + B  =  6

B  =  -2

so, A  =  8 and B  =  -2

By applying A  =  8 and B  =  -2 in linear equation,

M  =  8n - 2

Therefore, the formula is M  =  8n - 2

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