Chapter 3.9, Problem 3OE

To determine

To Find: The missing entries in the table.

Answer to Problem 3OE

The answer is 3 and 2.

Explanation of Solution

Given information:Given values is a linear function.

Calculation:

Let the given linear function is $f(x)=ax+b$

From the table, we get

  $\begin{array}{l}\text{when}x=0\text{we}\text{get}f(x)=5\text{put}\text{these}\text{values}\text{on}\text{the}\text{above}\text{function}\\ 5=a\times 0+b\\ b=5\mathrm{...}(1)\\ \text{Similarly,}\\ \text{when}x=2\text{we}\text{get}f(x)=4,\text{than}\\ 4=a\times 2+b\\ 2a+b=4\mathrm{...}(2)\\ 2a+5=4\text{from}(1)\\ 2a=4-5\\ a=\frac{-1}{2}\\ a=-0.5\end{array}$

So, the required function is $f(x)=-0.5x+5$

Now,

  $\begin{array}{l}\text{when}x=4\\ f(x)=-0.5\times 4+5\\ f(x)=-2+5\\ f(x)=3\\ \text{and}\text{when}x=6\\ f(x)=-0.5\times 6+5\\ f(x)=-3+5\\ f(x)=2\end{array}$

Thus, the missing values are 3 and 2.