Maths-
General
Easy

Question

How can you determine whether the data in the table can be modelled by a linear function ?

hintHint:

1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.
2. When the difference between 2 consecutive differences for output values (y values) for a given constant change in the input values (x values) is constant. i.e. dy(n)- dy(n-1) is constant for any value of n, the function is known as a quadratic function.
3. When the ratio between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant i.e. fraction numerator y left parenthesis n right parenthesis over denominator y left parenthesis n minus 1 right parenthesis end fraction is constant for any value of n, the function is known as an exponential function.

The correct answer is: The given function is a linear function.


    Step-by-step solution:-

    From the given table, we observe the following readings-

    x1 = -2, y1 = -1;
    x2 = -1, y2 = 1;
    x3 = 0, y3 = 3;
    x4 = 1, y4 = 5;
    x5 = 2, y5 = 7
    a). Difference between 2 consecutive x values-
                                                                                  dx1 = x2 - x1 = -1 - (-2) = -1 + 2 = 1
                                                                                   dx2 = x3 - x2 = 0 - (-1) = 0 + 1 = 1
                                                                                           dx3 = x4 - x3 = 1 - 0 = 1
                                                                                           dx4 = x5 - x4 = 2 - 1 = 1
    Difference between 2 consecutive y values-
                                                                                   dy1 = y2 - y1 = 1 - (-1) = 1 + 1 = 2
                                                                                           dy2 = y3 - y2 = 3 - 1 = 2
                                                                                           dy3 = y4 - y3 = 5 - 3 = 2
                                                                                           dy4 = y5 - y4 = 7 - 5 = 2
    We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is constant i.e. 1.
    Hence, the given function is a linear function.
    Final Answer:-
    ∴ The given function is a linear function.

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