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Sagot :

Take some points

  • 2x+3y<6
  • 3y<-2x+6
  • y<-2/3x+2

As here < sign present line will be dashed and shading should be done below the line

So

  • (1,1)
  • (1,0)
  • (2,0)
  • (-1,2)

Graph attached

View image Аноним
semsee45

Answer:

Given inequality

[tex]\sf 2x + 3y < 6[/tex]

Rearrange to make y the subject

[tex]\sf \implies 2x + 3y < 6[/tex]

Subtract 2x from both sides:

[tex]\sf \implies 3y < -2x + 6[/tex]

Divide both sides by 3:

[tex]\sf \implies y < -\dfrac23x + 2[/tex]

When graphing inequalities

If the inequality sign is < or > then the line of the graph should be dashed.

If the inequality sign is ≤ or ≥ then the line of the graph should be solid.

If y < (less than) then the shading is below the line.

If y > (more than) then the shading is above the line.

Therefore, as the inequality is y < the line should be dashed and the shading should be below the dashed line.

To plot the line, substitute x = 0 and x = 3 into the equation:

[tex]\sf \implies -\dfrac23(0) + 2=2[/tex]

[tex]\sf \implies -\dfrac23(3) + 2=0[/tex]

Therefore, plot points (0, 2) and (3, 0).  Draw a dashed straight line through the points.  Shade below the dashed line.

View image semsee45
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