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Math Worksheets | Dynamically Created Math Worksheets

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Show Answer Key & Explanations Step-by-step solution for: Math Worksheets | Dynamically Created Math Worksheets
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Let's solve each function table step by step. We'll plug in the given $ x $-values into the corresponding equation to find the $ y $-values.

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1) $ y = \frac{1}{6}x + 6 $



| $ x $ | $ y = \frac{1}{6}x + 6 $ |
|--------|---------------------------|
| 3 | $ \frac{1}{6}(3) + 6 = 0.5 + 6 = 6.5 $ ✔ |
| -1 | $ \frac{1}{6}(-1) + 6 = -0.1667 + 6 = 5.8333 $ ✔ |
| 6 | $ \frac{1}{6}(6) + 6 = 1 + 6 = 7 $ ✔ |
| -9 | $ \frac{1}{6}(-9) + 6 = -1.5 + 6 = 4.5 $ ✔ |
| 1 | $ \frac{1}{6}(1) + 6 = 0.1667 + 6 = 6.1667 $ (given as 6.167) ✔ |

✔ Already correct.

---

2) $ y = x + 2 $



| $ x $ | $ y = x + 2 $ |
|--------|----------------|
| 9 | $ 9 + 2 = 11 $ |
| -4 | $ -4 + 2 = -2 $ |
| 2 | $ 2 + 2 = 4 $ |
| 8 | $ 8 + 2 = 10 $ |
| -5 | $ -5 + 2 = -3 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| 9 | 11 |
| -4 | -2 |
| 2 | 4 |
| 8 | 10 |
| -5 | -3 |

---

3) $ y = -7x - 3 $



| $ x $ | $ y = -7x - 3 $ |
|--------|-------------------|
| 2 | $ -7(2) - 3 = -14 - 3 = -17 $ |
| 6 | $ -7(6) - 3 = -42 - 3 = -45 $ |
| 3 | $ -7(3) - 3 = -21 - 3 = -24 $ |
| -2 | $ -7(-2) - 3 = 14 - 3 = 11 $ |
| 8 | $ -7(8) - 3 = -56 - 3 = -59 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| 2 | -17 |
| 6 | -45 |
| 3 | -24 |
| -2 | 11 |
| 8 | -59 |

---

4) $ y = -\frac{1}{3}x - 9 $



| $ x $ | $ y = -\frac{1}{3}x - 9 $ |
|--------|-----------------------------|
| 0 | $ -\frac{1}{3}(0) - 9 = -9 $ |
| -9 | $ -\frac{1}{3}(-9) - 9 = 3 - 9 = -6 $ |
| 2 | $ -\frac{1}{3}(2) - 9 = -0.6667 - 9 = -9.6667 $ |
| 9 | $ -\frac{1}{3}(9) - 9 = -3 - 9 = -12 $ |
| 5 | $ -\frac{1}{3}(5) - 9 = -1.6667 - 9 = -10.6667 $ |

Answer:
| $ x $ | $ y $ |
|--------|---------------|
| 0 | -9 |
| -9 | -6 |
| 2 | -9.6667 |
| 9 | -12 |
| 5 | -10.6667 |

(Or as fractions: $ -\frac{29}{3} $, $ -\frac{32}{3} $)

---

5) $ y = 7x $



| $ x $ | $ y = 7x $ |
|--------|-------------|
| -9 | $ 7(-9) = -63 $ |
| 3 | $ 7(3) = 21 $ |
| -2 | $ 7(-2) = -14 $ |
| 5 | $ 7(5) = 35 $ |
| 9 | $ 7(9) = 63 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| -9 | -63 |
| 3 | 21 |
| -2 | -14 |
| 5 | 35 |
| 9 | 63 |

---

6) $ y = -5x $



| $ x $ | $ y = -5x $ |
|--------|--------------|
| 0 | $ -5(0) = 0 $ |
| -4 | $ -5(-4) = 20 $ |
| 4 | $ -5(4) = -20 $ |
| 1 | $ -5(1) = -5 $ |
| 2 | $ -5(2) = -10 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| 0 | 0 |
| -4 | 20 |
| 4 | -20 |
| 1 | -5 |
| 2 | -10 |

---

7) $ y = -2x - 4 $



| $ x $ | $ y = -2x - 4 $ |
|--------|-------------------|
| 3 | $ -2(3) - 4 = -6 - 4 = -10 $ |
| -7 | $ -2(-7) - 4 = 14 - 4 = 10 $ |
| -9 | $ -2(-9) - 4 = 18 - 4 = 14 $ |
| 1 | $ -2(1) - 4 = -2 - 4 = -6 $ |
| -4 | $ -2(-4) - 4 = 8 - 4 = 4 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| 3 | -10 |
| -7 | 10 |
| -9 | 14 |
| 1 | -6 |
| -4 | 4 |

---

8) $ y = x + 4 $



| $ x $ | $ y = x + 4 $ |
|--------|----------------|
| -7 | $ -7 + 4 = -3 $ |
| -8 | $ -8 + 4 = -4 $ |
| 3 | $ 3 + 4 = 7 $ |
| 4 | $ 4 + 4 = 8 $ |
| -1 | $ -1 + 4 = 3 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| -7 | -3 |
| -8 | -4 |
| 3 | 7 |
| 4 | 8 |
| -1 | 3 |

---

9) $ y = x - 8 $



| $ x $ | $ y = x - 8 $ |
|--------|----------------|
| 2 | $ 2 - 8 = -6 $ |
| -3 | $ -3 - 8 = -11 $ |
| -6 | $ -6 - 8 = -14 $ |
| 1 | $ 1 - 8 = -7 $ |
| 0 | $ 0 - 8 = -8 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| 2 | -6 |
| -3 | -11 |
| -6 | -14 |
| 1 | -7 |
| 0 | -8 |

---

10) $ y = -\frac{1}{4}x + 8 $



| $ x $ | $ y = -\frac{1}{4}x + 8 $ |
|--------|-----------------------------|
| 0 | $ 0 + 8 = 8 $ |
| -8 | $ -\frac{1}{4}(-8) + 8 = 2 + 8 = 10 $ |
| 5 | $ -\frac{1}{4}(5) + 8 = -1.25 + 8 = 6.75 $ |
| -9 | $ -\frac{1}{4}(-9) + 8 = 2.25 + 8 = 10.25 $ |
| -2 | $ -\frac{1}{4}(-2) + 8 = 0.5 + 8 = 8.5 $ |

Answer:
| $ x $ | $ y $ |
|--------|-------------|
| 0 | 8 |
| -8 | 10 |
| 5 | 6.75 |
| -9 | 10.25 |
| -2 | 8.5 |

---

11) $ y = 5x + 5 $



| $ x $ | $ y = 5x + 5 $ |
|--------|------------------|
| -2 | $ 5(-2) + 5 = -10 + 5 = -5 $ |
| -3 | $ 5(-3) + 5 = -15 + 5 = -10 $ |
| 3 | $ 5(3) + 5 = 15 + 5 = 20 $ |
| -7 | $ 5(-7) + 5 = -35 + 5 = -30 $ |
| -8 | $ 5(-8) + 5 = -40 + 5 = -35 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| -2 | -5 |
| -3 | -10 |
| 3 | 20 |
| -7 | -30 |
| -8 | -35 |

---

12) $ y = -9x $



| $ x $ | $ y = -9x $ |
|--------|--------------|
| 0 | $ -9(0) = 0 $ |
| -7 | $ -9(-7) = 63 $ |
| 6 | $ -9(6) = -54 $ |
| 5 | $ -9(5) = -45 $ |
| -3 | $ -9(-3) = 27 $ |

Answer:
| $ x $ | $ y $ |
|--------|--------|
| 0 | 0 |
| -7 | 63 |
| 6 | -54 |
| 5 | -45 |
| -3 | 27 |

---

✔ Final Answer Summary:



Here are all completed tables:

1) ✔️ Done
2)
| x | y |
|---|---|
| 9 | 11 |
| -4 | -2 |
| 2 | 4 |
| 8 | 10 |
| -5 | -3 |

3)
| x | y |
|---|---|
| 2 | -17 |
| 6 | -45 |
| 3 | -24 |
| -2 | 11 |
| 8 | -59 |

4)
| x | y |
|---|----|
| 0 | -9 |
| -9 | -6 |
| 2 | -9.6667 |
| 9 | -12 |
| 5 | -10.6667 |

5)
| x | y |
|---|---|
| -9 | -63 |
| 3 | 21 |
| -2 | -14 |
| 5 | 35 |
| 9 | 63 |

6)
| x | y |
|---|---|
| 0 | 0 |
| -4 | 20 |
| 4 | -20 |
| 1 | -5 |
| 2 | -10 |

7)
| x | y |
|---|---|
| 3 | -10 |
| -7 | 10 |
| -9 | 14 |
| 1 | -6 |
| -4 | 4 |

8)
| x | y |
|---|---|
| -7 | -3 |
| -8 | -4 |
| 3 | 7 |
| 4 | 8 |
| -1 | 3 |

9)
| x | y |
|---|---|
| 2 | -6 |
| -3 | -11 |
| -6 | -14 |
| 1 | -7 |
| 0 | -8 |

10)
| x | y |
|---|----|
| 0 | 8 |
| -8 | 10 |
| 5 | 6.75 |
| -9 | 10.25 |
| -2 | 8.5 |

11)
| x | y |
|---|---|
| -2 | -5 |
| -3 | -10 |
| 3 | 20 |
| -7 | -30 |
| -8 | -35 |

12)
| x | y |
|---|---|
| 0 | 0 |
| -7 | 63 |
| 6 | -54 |
| 5 | -45 |
| -3 | 27 |

---

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