Chapter 9.7, Problem 35STP

To determine

Whether the equation for area of square represents linear or non-linear function

Answer to Problem 35STP

The equation for the area of square represents a non-linear function.

Explanation of Solution

The equation for area of square is $A=s^2$ , where ‘A’ is Area and ‘s’ is side of the square.

Linear Functions: The graph of linear functions is always a straight line. These functions have the form $y=a+bx$ .

The equation of the area of square is not in the form $y=a+bx$ .

Also, the table for the values of ‘s’ and corresponding values of ‘A’ can be drawn as:

‘s’ (Side)	‘A’ (Area)
1	1
2	4
3	9
4	16
5	25
6	36
7	49

The slope of the linear function always remains constant. The slope of the data in above table is given by:

  $m=\frac{A_2-A_1}{s_2-s_1}$

From the given table,

  $\begin{array}{l}{m}_1=\frac{4-1}{2-1}\\ m_1=\frac{3}{1}=3\\ \\ m_2=\frac{9-4}{3-2}\\ m_2=\frac{5}{1}=5\\ \\ m_3=\frac{16-9}{4-3}\\ m_3=\frac{7}{1}=7\end{array}$

As m1 is not equal to m2 is not equal to m3, the slope is not constant, hence, the data represents a non-linear function.