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.
