Chapter 5.6, Problem 28E

To determine

To draw: the graph the inequality in a coordinate plane.

Explanation of Solution

Given information: We have given an inequality $3x-y\ge 5$

Procedure: First change given equality into slope- intercept form

Subtract 3x both sides

  $\begin{array}{l}3x-y-3x\ge 5-3x\\ \Rightarrow -y\ge 5-3x\end{array}$

Multiply by -1 on both sides

  $\begin{array}{l}-1\left(-y\right)\ge -1\left(5-3x\right)\\ \Rightarrow y\le 3x-5\end{array}$

We switched the inequality sign for multiplying by a negative number.

The slope −intercept form is $y=mx+b$ , where m is the slope and b is the y -intercept.

We find the values of  m  and  b  for $y\le 3x-5$ , we get

  $\begin{array}{l}m=3\\ b=-5\end{array}$

So, the slope of the line is 3 and the y −intercept is -5.

Plot y -intercept (0,-5) first.

Plot one more point using $\frac{Rise}{Run}=\frac{3}{1}.$

Another coordinate will be $\left(0+1,-5+3\right)=(1,-2).$

For $\le$ inequality sign draw a solid line by joining the points (0, -5)) and $(1,-2)$ and shade down the solid line.