Chapter 1.8, Problem 4CFU

To determine

To graph: the given inequality.

Answer to Problem 4CFU

  

Explanation of Solution

Given information:

  $x+y<4$

Calculation:

Rearrange the inequality as follows:

  $y<-x+4$

For line $y=-x+4$ , the slope is $-1$ and the y-intercept is 4.

Create a table by plugging the different values x in the line equation to evaluate the value for y.

$x$	-4	-3	-2	-1	0	1	2	3	4
$y$	8	7	6	5	4	3	2	1	0

Since the inequality has less than sign (<), dotted line will be used to graph a line $y=-x+4$ .

Put the test points (0,0) and (3,2) in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $y<-x+4$	True/False test point
$\left(0,0\right)$	$\begin{array}{l}0<-0+4\\ 0<4\end{array}$	True
$\left(3,2\right)$	$\begin{array}{l}2<-3+4\\ 2<1\end{array}$	False

The graph for the given inequality is shown below.