Chapter SH, Problem 3.18EP

To determine

To find the function is linear or not.

  

Answer to Problem 3.18EP

Not a linear function.

Explanation of Solution

Given information:

The function is

  

Formula used:

  $\frac{\Delta y}{\Delta x}=\frac{y_1-y_0}{x_1-x_0}$

Where,

  $\Delta y$ is change in y

  $\Delta x$ is change in x

Calculation:

Rate of change in y correspond to rate of change in x for first two terms of x and y

  $\frac{\Delta y}{\Delta x}=\frac{2-14}{4-7}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{12}{3}$

Rate of change in y correspond to rate of change in x for second and third terms of x and y

  $\frac{\Delta y}{\Delta x}=\frac{12-2}{1-4}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{10}{3}$

Rate of change in y correspond to rate of change in x for third and fourth terms of x and y

  $\frac{\Delta y}{\Delta x}=\frac{4-12}{-2-1}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{8}{3}$

Rate of change in y correspond to rate of change in x for fourth and fifth terms of x and y

  $\frac{\Delta y}{\Delta x}=\frac{10-4}{-5-(-2)}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{6}{-3}$

There is not a constant change of in x corresponds to a constant change of in y.

So, these points does not satisfy a linear function.

Hence, is a non linear function.