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Use the linear inequality + 8y 24 for Part A, Part B, and Part C. Part A: Determine the boundary line, and state whether the line will be dashed or solid. Part B: Which half-plane should be shaded? Describe where you should shade using the language "above" or "below" the line. Part C: Show your work for Part B to show how you determined which half-plane to shade.​

Use the linear inequality 8y 24 for Part A Part B and Part C Part A Determine the boundary line and state whether the line will be dashed or solid Part B Which class=

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Answer:

Given inequality:  [tex]x+8y\leq 24[/tex]

Part A

Solid line: ≤ or ≥

Dashed line: < or >

Therefore, the line will be solid.

Part B

Shading above the line: y > or y ≥

Shading below the line: y < or y ≤

Therefore, shade below the line.

Part C

Make y the subject to determine where to shade.

Given inequality:  

[tex]x+8y\leq 24[/tex]

Subtract x from both sides:

[tex]8y\leq 24-x[/tex]

Divide both sides by 8:

[tex]y\leq 3-\dfrac18x[/tex]

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[tex]\\ \rm\Rrightarrow x+8y\leqslant 24[/tex]

#Part A

  • as ≤ is present line will be dashed

#Part B

Put (0,0)

  • 0+8(0)≤24
  • 0≤24

Satisfied

Shading below the line and towards origin

#Part C

turn into y=mx+b form

  • 8y≤-x+24
  • y≤-1/8x+3

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