Chapter 3.9, Problem 24WE

To determine

To Find:The missing values of the given table.

Answer to Problem 24WE

The missing values of the table are $x_3=0$ & $y_4=-5$ .

Explanation of Solution

Given information:The table is given below

  

Form the table it can be observed that when x changes from (2 to 4), g ( x ) changes from (1 to 4).

  $m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}=\frac{\left(4-1\right)}{\left(4-2\right)}=\frac{3}{2}$

Then when g ( x ) changes from (4 to -2), x will be

  $\begin{array}{l}m=\frac{\left(-2-4\right)}{\left(x_3-4\right)}\\ \frac{3}{2}=\frac{\left(-6\right)}{\left(x_3-4\right)}\\ 3\left(x_3-4\right)=-12\\ 3x_3-12=-12\\ x_3=0\end{array}$

Hence the value of $x_3=0$ .

Then when x changes from (0 to -2), g ( x ) will be

  $\begin{array}{l}m=\frac{\left(y_4-\left(-2\right)\right)}{\left(-2-0\right)}\\ \frac{3}{2}=-\frac{\left(y_4+2\right)}{2}\\ y_4+2=-3\\ y_4=-5\end{array}$

Hence the value of $y_4=-5$ .

Hence the missing values of the table are $x_3=0$ & $y_4=-5$ .