Question 1109406
1. {{{2x+3y <18}}} 

to graph the following inequality, first draw the line and decide which side to shade for the required region

Explanation:

Treat the inequality as an equality or as a straight line graph first. Then shade the correct side of the line to indicate the solutions which are less than {{{18}}}.

You can use any method to draw the straight line - plot points or use the intercept/gradient method.

I will use the method of the {{{x}}} and {{{y}}} intercepts.

To find the {{{x}}}-intercept, make {{{y=0}}}:
{{{2x+3y =18}}} 
{{{2x+3*0 =18}}} 
{{{2x =18}}} 
{{{x = 9}}} => {{{x}}}-intercept is at ({{{9}}},{{{0}}})

To find the {{{y}}}-intercept, make {{{x=0}}}
{{{2x+3y =18}}} 
{{{2*0+3y=18 }}}
{{{3y=18}}} 
{{{y= 6}}}=> {{{y}}}-intercept is at ({{{0}}},{{{6}}})

Now that you have both intercepts you can plot them and draw a solid line through them. This is the line {{{2x+3y =18}}}.
You could also write the equation as : {{{y=-(2/3)x+6}}}

{{{ graph( 600, 600, -10, 10, -10, 10, -(2/3)x+6) }}} 

To decide which side of the line to {{{shade}}}, choose a test point.

({{{0}}},{{{0}}}) is a good one to test:

since given: {{{2x+3y <18}}}, you have
{{{2*0+3*0 <18}}}  => {{{0<18}}} is {{{true}}}


so, ({{{0}}},{{{0}}}) is in the required region and the area BELOW the line must be shaded 

{{{ graph( 600, 600, -10, 10, -10, 10, 2x+3y <18) }}}


2. {{{3x-y <=6}}}...do it same way 
 
intercepts:

{{{3x-y =6}}}...set {{{y=0}}}
{{{3x-0 =6}}}
{{{x =2}}}=> {{{x}}}-intercept is at ({{{2}}},{{{0}}})

{{{3x-y =6}}}...set {{{x=0}}}
{{{3*0-y =6}}}
{{{y =-6}}}=> {{{y}}}-intercept is at ({{{0}}},{{{-6}}})

graph:{{{3x-y =6}}} or {{{y=3x-6}}}


{{{ graph( 600, 600, -10, 10, -10, 10, 3x-6) }}}

since given {{{3x-y <=6}}} solution is a line and all points to the left and above the line

{{{ graph( 600, 600, -10, 10, -10, 10, 3x-y <=6) }}}


3.
{{{y>= 0}}}-> here you have  graph shaded above {{{x}}}-axis including {{{x}}}-axis
{{{ graph( 600, 600, -10, 10, -10, 10, y >=0,y >=0) }}}

4.

{{{x>= 0}}}-> here you have  graph shaded starting with {{{y}}}-axis including everything to the right

{{{ graph( 600, 600, -10, 10, -10, 10, x >=0,x >=0) }}}