The correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values
The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
Given a table on which there are two column in which one column represents x values while other column represent the y values
We have to find whether the relationship between x value and y value is linear or exponential
From given table let,
y₁ = 34; y₂ = 41; y₃ = 48; y₄ = 55
x₁ = 1; x₂ = 2; x₃ = 3; x₄ = 4
If the relationship between the x value and y value is linear then the difference between two consecutive value of x value and y value would be equal
So y₂-y₁ = y₄-y₃ and x₂-x₁ = x₄-x₃
Putting the value we get difference of y value 7 and x value as 1 since it is same we can say that the relation ship between x value and y value is linear
Hence the correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values
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