Chapter 6.4, Problem 43SR

To determine

To graph the inequality.

Answer to Problem 43SR

Graph of the given inequality:

  

Explanation of Solution

Given information: We have given inequality $8x+y\le 6.$

Calculations: Change given inequality in slope-intercept form $y=mx+b$ first, where m is the slope and b is the y -intercept.

  $8x+y\le 6$

Subtracting 8x on both sides

  $8x+y-8x\le 6-8x$

Simplify

  $y\le -8x+6$

The slope of the line $y\le -8x+6$ is $-8$ and the y −intercept is 6.

Plot y-intercept $\left(0,6\right)$ first.

Plot one more point using $\frac{Rise}{Run}=\frac{-8}{1}.$

Another coordinate will be $\left(0+1,6-8\right)=(1,-2).$

For $\le$ inequality sign draw a solid line by joining the points $\left(0,6\right)$ and $(1,-2)$ and shade down the line.