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Let's solve the problem step by step based on the worksheet titled "Graphing Linear Inequalities" from Brighterly.com.

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🔹 Section A: Check whether each ordered pair is a solution of the graph

We are given 6 graphs, each with a line and a shaded region. For each graph, we must check if the given ordered pair lies within the shaded region, because only points in the shaded region (and possibly on the boundary, depending on the inequality) are solutions.

We will go through each one:

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#### 1) (-4, -1)

- Graph shows a solid line with positive slope.
- The shaded region is above the line.
- Plotting (-4, -1): x = -4, y = -1
- Check if this point is above the line.

From the graph:
- The line passes through (0, 2) and (2, 4), so slope = (4–2)/(2–0) = 1 → y = x + 2
- Plug in x = -4: y = -4 + 2 = -2
- So at x = -4, the line has y = -2
- Our point is (-4, -1), which has y = -1 > -2 → above the line
- Shaded region is above → ✔ Yes, it’s a solution

> ✔ Answer: Yes

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#### 2) (-8, 3)

- Graph: Line goes through (0, 0) and (2, 2) → y = x
- Shaded region is above the line
- Check point (-8, 3)
- At x = -8, line has y = -8
- Point has y = 3 > -8 → above the line → ✔ Yes

> ✔ Answer: Yes

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#### 3) (5, -6)

- Graph: Line goes from (0, 4) to (4, 0) → slope = (0–4)/(4–0) = -1 → y = -x + 4
- Shaded region is below the line (since it’s below)
- Check (5, -6)
- At x = 5, y = -5 + 4 = -1
- Point y = -6 < -1 → below the line → ✔ Yes

> ✔ Answer: Yes

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#### 4) (15, -9)

- Graph: Line appears to be horizontal? Let's see.
- Points: (0, 0), (2, 0), (4, 0) → seems like y = 0
- But shaded region is below the line (y < 0)
- Point (15, -9): y = -9 < 0 → ✔ Yes

> ✔ Answer: Yes

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#### 5) (1, 6)

- Line: Goes through (0, -2), (2, 2), (4, 6) → slope = (2+2)/2 = 2 → y = 2x - 2
- Shaded region is above the line
- Check (1, 6):
- On line: y = 2(1) - 2 = 0
- Point has y = 6 > 0 → above → ✔ Yes

> ✔ Answer: Yes

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#### 6) (7, 12)

- Line: Goes through (0, 0), (2, 3), (4, 6) → slope = 3/2 → y = (3/2)x
- Shaded region is above the line
- Check (7, 12):
- On line: y = (3/2)(7) = 10.5
- Point y = 12 > 10.5 → above → ✔ Yes

> ✔ Answer: Yes

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✔ Summary for Section A:

| # | Ordered Pair | Solution? |
|---|--------------|----------|
| 1 | (-4, -1) | Yes |
| 2 | (-8, 3) | Yes |
| 3 | (5, -6) | Yes |
| 4 | (15, -9) | Yes |
| 5 | (1, 6) | Yes |
| 6 | (7, 12) | Yes |

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🔹 Section B: Check whether each ordered pair is a solution of the graph

Now we have one graph with multiple points to test.

Look at the graph:
- It shows a dashed line (so strict inequality, no equality)
- Line goes through (0, 2), (2, 4), (4, 6) → slope = 1 → y = x + 2
- Shaded region is below the line → inequality is y < x + 2
- Dashed line → not inclusive (no equal)

Now test each point:

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#### 1) (-2, -8)

- Plug into y < x + 2
- Left: y = -8
- Right: x + 2 = -2 + 2 = 0
- Is -8 < 0? ✔ Yes
- Also, check if point is below the line → yes
- But wait: is it in the shaded region?

From graph: at x = -2, line has y = 0 → point (-2, -8) is way below → ✔ Yes

> ✔ Answer: Yes

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#### 2) (12, -10)

- y = -10
- x + 2 = 12 + 2 = 14
- Is -10 < 14? ✔ Yes
- Point is far below → ✔ Yes

> ✔ Answer: Yes

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#### 3) (14, 2)

- y = 2
- x + 2 = 14 + 2 = 16
- Is 2 < 16? ✔ Yes
- Still below → ✔ Yes

> ✔ Answer: Yes

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#### 4) (-3, 4)

- y = 4
- x + 2 = -3 + 2 = -1
- Is 4 < -1? ✘ No
- 4 > -1 → point is above the line → not in shaded region

> ✘ Answer: No

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#### 5) (6, -14)

- y = -14
- x + 2 = 6 + 2 = 8
- Is -14 < 8? ✔ Yes
- Below line → ✔ Yes

> ✔ Answer: Yes

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#### 6) (0, -12)

- y = -12
- x + 2 = 0 + 2 = 2
- Is -12 < 2? ✔ Yes
- Far below → ✔ Yes

> ✔ Answer: Yes

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✔ Summary for Section B:

| # | Ordered Pair | Solution? |
|---|--------------|----------|
| 1 | (-2, -8) | Yes |
| 2 | (12, -10) | Yes |
| 3 | (14, 2) | Yes |
| 4 | (-3, 4) | No |
| 5 | (6, -14) | Yes |
| 6 | (0, -12) | Yes |

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✔ Final Answers:

#### Section A:
1. Yes
2. Yes
3. Yes
4. Yes
5. Yes
6. Yes

#### Section B:
1. Yes
2. Yes
3. Yes
4. No
5. Yes
6. Yes

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📝 Explanation:

To determine if an ordered pair is a solution:
1. Locate the point on the graph.
2. Check if it lies in the shaded region.
3. If the line is dashed, the boundary is not included.
4. If the line is solid, the boundary is included.
5. Use substitution into the inequality if needed.

In this case, all points in Section A were in the shaded regions, and most in Section B were below the dashed line (which is correct for y < x + 2), except (-3, 4), which is above.

✔ All done!