Question

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.​

Answer 1

`\\ \rm\Rrightarrow x+8y\leqslant 24`

#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

Answer 2

Given inequality:
`x+8y\leq 24`

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:

`x+8y\leq 24`

Subtract x from both sides:

`8y\leq 24-x`

Divide both sides by 8:

`y\leq 3-\frac18x`