Question

Does the table below represent a linear or nonlinear function?

Inches ___________ Centimeters
1_________________ 2.54
2_________________ 5.08
3_________________ 7.62
4_________________ 10.16

Answer 1

Answer: (B) Linear Functions is the correct answer.

Answer 2

Function assigns the value of one set to another. The table represents a linear function.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

A linear function is a function that follows the equation of a line, therefore, all the points lie on the line of the function. Therefore, every value of x will give a specific value of y and will follow

y = mx+c

where m is the slope of the line, and c is the value of the constant.

Let's take the first two coordinates (1, 2.54) and (2, 5.08), to find the slope of the line,

$y = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{5.08-2.54}{2-1} = 2.54$

Now, substitute the value of any one of the coordinates to get the value of the constant c,

$y = mx+c\\\\2.54 = 2.54(1)+c\\\\c = 0$

Thus, the equation of the line is y=2.54x+0 or y = 2.54x.

Now, check the value of the other two coordinates in the equation of the line we got,

(3, 7.62)

$y = 2.54x\\7.62 = 2.54(3)\\7.62 = 7.62$

(4, 10.16)

$y = 2.54x\\10.16= 2.54(4)\\10.16=10.16$

As all the coordinates are following the equation of the line, therefore, the table represents a linear function.

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