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