Chapter 3.3, Problem 25E

To determine

To graph the linear function:

$d\left(x\right)=-\frac{1}{2}x-3$

Answer to Problem 25E

Explanation of Solution

Given:

$d\left(x\right)=-\frac{1}{2}x-3$

Concept Used:

To graph a linear function $f\left(x\right)=ax+b$ :

1. Make an input-output table to find ordered pairs.
2. Plot the ordered pairs.
3. Draw a line through the points in above step.

Calculation:

In order graph the linear function:

$d\left(x\right)=-\frac{1}{2}x-3$

First, make an input-output table, by finding value of $d\left(x\right)$ at some values of x, say at $x=-2,-1,0,\text{ 1, and 2}$ As,

$\begin{array}{c}d\left(-2\right)=-\frac{1}{2}\times \left(-2\right)-3\\ =1-3\\ =-2,\\ d\left(-1\right)=-\frac{1}{2}\times \left(-1\right)-3\\ =\frac{1}{2}-3\\ =\frac{1-6}{2}\\ =\frac{-5}{2}\\ =-2.5\end{array}$

$\begin{array}{c}d\left(0\right)=-\frac{1}{2}\times \left(0\right)-3\\ =0-3\\ =-3,\\ d\left(1\right)=-\frac{1}{2}\times \left(1\right)-3\\ =-\frac{1}{2}-3\\ =\frac{-1-6}{2}\\ =\frac{-7}{2}\\ =-3.5,\text{ and }\\ d\left(2\right)=-\frac{1}{2}\times 2-3\\ =-1-3\\ =-4\end{array}$

Thus, input output table of given linear function is:

$x$	$-2$	$-1$	0	1	2
$d\left(x\right)$	$-2$	$-2.5$	$-3$	$-3.5$	$-4$

This input-output table gives the ordered pairs that satisfies graph of the given function: $\left(-2,-2\right),\left(-1,-2.5\right),\left(0,-3\right),\left(1,-3.5\right),\left(2,-4\right)$ .

Now finally to draw the graph of given linear function plot these ordered pair using a graphing utility and draw a line through them. The graph is represented as: