Step: 1

A table is said to form a linear function if the ratio of change in input to output is same through out the table.

Step: 2

In the first table C h a n g e i n f ( x ) C h a n g e i n x is not same through out. So, it is ruled out.

Step: 3

Step: 4

The change in input (x ) is 3 and the change in output f (x ) is 4.

Step: 5

Step: 6

In the third and fourth tables C h a n g e i n f ( x ) C h a n g e i n x is not same through out. So, they are ruled out.

Step: 7

Therefore,among the choices, table-2 forms a linear function.

Correct Answer is : Table 2

Step: 1

A table is said to form a linear function if the ratio of change in output to input is same throughout the table.

Step: 2

In the tables 1, 3, 4, and 5, c h a n g e i n f ( x ) c h a n g e i n x is same throughout.

Step: 3

So, tables 1, 3, 4, and 5 represents linear functions except table 2.

Step: 4

So, table 2 represents a non-linear function.

Correct Answer is : Table 2

Step: 1

An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.

Step: 2

Among the choices, the equation 2 + 3x = 4 is a linear equation.

Correct Answer is : 2 + 3x = 4

Step: 1

A table is said to form a non-linear function if the ratio of change in output to input is same throughout the table.

Step: 2

In the tables 1, 2 and 4, c h a n g e i n f ( x ) c h a n g e i n x is not same throughout.

Step: 3

[Consider table 3.]

Step: 4

The change in input (x ) is 1 and the change in output f (x ) is 2.

Step: 5

Step: 6

Among the choices, Table 3 forms a linear function.

[The ratio of the change in f (x ) to the change in x is same throughout the table.]

Correct Answer is : Table 3

(i) 4

(ii) 2

(iii)

Step: 1

A linear function is of the form y = mx + b .

Step: 2

4x + y - 6 = 0 gives y = 6 - 4x

[Keep 'y' on one side, bring the rest to the other side.]

Step: 3

2y - (12 x ) = 1 gives y = (6 x ) + 1 2

Step: 4

Step: 5

Among the given equations, only 4x + y - 6 = 0 represents a linear function.

Correct Answer is : only (i)

Step: 1

A function in the form of f (x ) = m x + c is called a linear function.

[In a linear function, the exponent of x must be 1.]

Step: 2

Among the choices 3x ^{2} = 15 is not in the form of a linear function.

[The exponent of x is 2.]

Step: 3

So, the equation in choice B is not a linear function.

Correct Answer is : 3x ^{2} = 15

Step: 1

A linear function is of the form y = m x + b .

Step: 2

[Keep 'y' on one side, bring the rest to the other side.]

Step: 3

5y - (19 x ) = 12 gives y = (19 5x ) + 12 5

Step: 4

9x y - 2 = 0 gives y = 2 9 x

Step: 5

Step: 6

So, x + y - 4 = 0 represents a linear function.

Correct Answer is : x + y - 4 = 0

Step: 1

An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.

Step: 2

In the equation (2x - 7)^{3} = 26, x is raised to the power 3.

Step: 3

So, (2x - 7)^{3} = 26 is not a linear equation.

Correct Answer is : (2x - 7)^{3} = 26

Step: 1

An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.

Step: 2

In the equation (x - 3)^{2} = 9, x is raised to the power 2.

Step: 3

So, (x - 3)^{2} = 9 is not a linear equation.

Correct Answer is : (x - 3)^{2} = 9

Step: 1

Step: 2

In the equation x ^{2} - 5x - 6 = 0, x is raised to the power 2.

Step: 3

So, x ^{2} - 5x - 6 = 0 is not a linear equation.

Correct Answer is : x ^{2} - 5x - 6 = 0

Step: 1

A linear function is function that can be written as y = m x + c .

Step: 2

Interest for an amount of $P at r % rate of interest for 2 years can be written as I = P (1 + r 1 0 0 )^{2} - P , which is not a linear function.

Step: 3

Among the choices given, 'Interest for an amount of $P at r % rate of interest for 2 years' is not a linear function.

Correct Answer is : Interest for an amount of $P at r % rate of interest for 2 years.

Step: 1

Step: 2

In the equation x ^{4} - 2 = 23, x is raised to the power 4.

Step: 3

So, x ^{4} - 2 = 23 is not a linear equation.

Correct Answer is : x ^{4} - 2 = 23

Step: 1

An equation of the form a x + b y = c where either a ≠
0 or b ≠ 0 is the linear equation.

Step: 2

Hence, from the given choices, '- 5x - y = - 1 6 ', is the linear equation.

Correct Answer is : - 5x - y = - 1 6

Step: 1

Step: 2

In the equation (x + 4)^{3} = 9, x is raised to the power 3.

Step: 3

So, (x + 4)^{3} = 9 is not a linear equation.

Correct Answer is : (x + 4)^{3} = 9

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