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.
Learn more about Function:
https://brainly.com/question/5245372
