Question

Please help solve questions

Answer 1

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

Answer 2

Given inequality

`\sf 2x + 3y < 6`

Rearrange to make y the subject

`\sf \implies 2x + 3y < 6`

Subtract 2x from both sides:

`\sf \implies 3y < -2x + 6`

Divide both sides by 3:

`\sf \implies y < -\frac23x + 2`

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:

`\sf \implies -\frac23(0) + 2=2`

`\sf \implies -\frac23(3) + 2=0`

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