Chapter SH, Problem 3.17EP

To determine

To find the function is linear or not.

  

Answer to Problem 3.17EP

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

  $\frac{\Delta y}{\Delta x}=\frac{6-0}{0-(-2)}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{6}{2}$

Further solving,

  $\frac{\Delta y}{\Delta x}=3$

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

  $\frac{\Delta y}{\Delta x}=\frac{12-6}{2-0}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{6}{2}$

Further solving,

  $\frac{\Delta y}{\Delta x}=3$

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

  $\frac{\Delta y}{\Delta x}=\frac{18-12}{4-2}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{6}{2}$

Further solving,

  $\frac{\Delta y}{\Delta x}=3$

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

  $\frac{\Delta y}{\Delta x}=\frac{24-18}{6-4}$

On solving,

  $\frac{\Delta y}{\Delta x}=\frac{6}{2}$

Further solving,

  $\frac{\Delta y}{\Delta x}=3$

A constant change of +2 in x corresponds to a constant change of +6 in y.

So, these points satisfy a linear function.

Hence, is a linear function.