Chapter 9.7, Problem 30HP

To determine

A real-world situation that represents a linear function

Answer to Problem 30HP

A person’s bank account in which 1 lakh rupees are being deposited every month.

Explanation of Solution

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

The slope of the linear graph always remains constant. The slope of the equation is given by:

  $m=\frac{y_2-y_1}{x_2-x_1}$

The real-world situation which represents a linear function can be:

A person depositing 1 lakh rupees in his bank account every month. The table can be formed for this situation as given below:

Month (x)	Account Balance (y)
1	100000
2	200000
3	300000
4	400000
5	500000
6	600000
7	700000

From the given table, we can see that the slope, ‘m’, remains constant for all the values.

  $\begin{array}{l}{m}_1=\frac{200000-100000}{2-1}\\ m_1=\frac{100000}{1}=100000\\ \\ m_2=\frac{300000-200000}{3-2}\\ m_2=\frac{100000}{1}=100000\\ \\ m_3=\frac{400000-300000}{4-3}\\ m_3=\frac{100000}{1}=100000\end{array}$

As m1=m2=m3, the slope is constant, hence, the situation represents a linear function.