Chapter 6.4, Problem 40SR

To determine

To graph the inequality.

Answer to Problem 40SR

Graph of the given inequality:

  

Explanation of Solution

Given information: We have given inequality $6x+3y>12$

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

  $6x+3y>12$

Subtracting 6x from both sides

  $6x+3y-6x>12-6x$

Simplify

  $3y>-6x+12$

Dividing both sides by 3

  $$

  $\frac{3y}{3}>-\frac{6x}{3}+\frac{12}{3}$

Simplify

  $y>-2x+4$

The slope of the line $y=-2x+4$ is $-2$ and the y −intercept is 4.

Plot y-intercept $\left(0,4\right)$ first.

Plot one more point using $\frac{Rise}{Run}=-\frac{2}{1}.$

Another coordinate will be $\left(0+1,4-2\right)=(1,2).$

For > inequality sign draw a dotted line by joining the points $\left(0,4\right)$ and $(1,2)$ and shade up the line.