Chapter 3.1, Problem 9CYU

To determine

To Graph: The equation $x+2y=4$ by making a table and then state the domain and range.

Explanation of Solution

Given information:

The equation $x+2y=4$

Calculation:

The domain is all real numbers, which can be written as $D=\left(-\infty <x<\infty \right)$ . Select value from domain and make a table. Create ordered pairs and graph them. The range is also all real numbers or $R=\left(-\infty <x<\infty \right)$

We can rewrite the equation as $y=\frac{4-x}{2}$

x	$\frac{4-x}{2}$	y	$\left(x,y\right)$
-2	$\frac{4-\left(-2\right)}{2}$	3	$\left(-2,3\right)$
0	$\frac{4-0}{2}$	2	$\left(0,2\right)$
2	$\frac{4-2}{2}$	1	$\left(2,1\right)$
4	$\frac{4-4}{2}$	0	$\left(4,0\right)$

Therefore, Domain and Range are:

  $\begin{array}{l}D=\left\{-2,0,2,4\right\}\\ R=\left\{3,2,1,0\right\}\end{array}$