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asked Oct 18, 2023 83.9k views

2 Answers

JMelnik · Answer 1 · 2023-10-20T07:49:40+0000

Take some points

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

So

Graph attached

Andrey Marchuk · Answer 2 · 2023-10-24T19:40:10+0000

Answer:

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.