29) through: $$ (3,-1) $$ and $$ (-4,-1) $$ 30) through: $$ (5,5) $$ and $$ (-2,0) $$ 1) through: $$ (0,-5) $$ and $$ (-2,-5) $$ 32) through: $$ (-4,2) $$ and $$ (-2,1) $$ 3) through: $$ (0,4) $$ and $$ (-3,1) $$ 34) through: $$ (0,-4) $$ and $$ (-2,-1) $$ 5) through: $$ (-4,-4) $$ and $$ (0,-3) $$ 36) through: $$ (0,1) $$ and $$ (-2,5) $$ 7) through: $$ (-1,-1) $$ and $$ (-3,0) $$ 38) through: $$ (0,3) $$ and $$ (-4,2) $$ 9) through: $$ (-5,0) $$ and $$ (-5,-3) $$ 40) through: $$ (2,0) $$ and $$ (-4,5) $$

Question

UpStudy AI · Accepted Answer

Sure! Below are the equations of the lines passing through each pair of points you've provided:

---

**1)** Through: $$ (0, -5) $$ and $$ (-2, -5) $$

- **Type:** Horizontal Line
- **Equation:** 
  $$
  y = -5
  $$

---

**3)** Through: $$ (0, 4) $$ and $$ (-3, 1) $$

- **Slope Calculation:**
  $$
  m = \frac{1 - 4}{-3 - 0} = \frac{-3}{-3} = 1
  $$
- **Equation:**
  $$
  y = x + 4
  $$

---

**5)** Through: $$ (-4, -4) $$ and $$ (0, -3) $$

- **Slope Calculation:**
  $$
  m = \frac{-3 - (-4)}{0 - (-4)} = \frac{1}{4}
  $$
- **Equation:**
  $$
  y = \frac{1}{4}x - 3
  $$

---

**7)** Through: $$ (-1, -1) $$ and $$ (-3, 0) $$

- **Slope Calculation:**
  $$
  m = \frac{0 - (-1)}{-3 - (-1)} = \frac{1}{-2} = -\frac{1}{2}
  $$
- **Equation:**
  $$
  y = -\frac{1}{2}x - \frac{3}{2}
  $$

---

**9)** Through: $$ (-5, 0) $$ and $$ (-5, -3) $$

- **Type:** Vertical Line
- **Equation:** 
  $$
  x = -5
  $$

---

**29)** Through: $$ (3, -1) $$ and $$ (-4, -1) $$

- **Type:** Horizontal Line
- **Equation:** 
  $$
  y = -1
  $$

---

**30)** Through: $$ (5, 5) $$ and $$ (-2, 0) $$

- **Slope Calculation:**
  $$
  m = \frac{0 - 5}{-2 - 5} = \frac{-5}{-7} = \frac{5}{7}
  $$
- **Equation:**
  $$
  y = \frac{5}{7}x + \frac{10}{7}
  $$

---

**32)** Through: $$ (-4, 2) $$ and $$ (-2, 1) $$

- **Slope Calculation:**
  $$
  m = \frac{1 - 2}{-2 - (-4)} = \frac{-1}{2} = -\frac{1}{2}
  $$
- **Equation:**
  $$
  y = -\frac{1}{2}x
  $$

---

**34)** Through: $$ (0, -4) $$ and $$ (-2, -1) $$

- **Slope Calculation:**
  $$
  m = \frac{-1 - (-4)}{-2 - 0} = \frac{3}{-2} = -\frac{3}{2}
  $$
- **Equation:**
  $$
  y = -\frac{3}{2}x - 4
  $$

---

**36)** Through: $$ (0, 1) $$ and $$ (-2, 5) $$

- **Slope Calculation:**
  $$
  m = \frac{5 - 1}{-2 - 0} = \frac{4}{-2} = -2
  $$
- **Equation:**
  $$
  y = -2x + 1
  $$

---

**38)** Through: $$ (0, 3) $$ and $$ (-4, 2) $$

- **Slope Calculation:**
  $$
  m = \frac{2 - 3}{-4 - 0} = \frac{-1}{-4} = \frac{1}{4}
  $$
- **Equation:**
  $$
  y = \frac{1}{4}x + 3
  $$

---

**40)** Through: $$ (2, 0) $$ and $$ (-4, 5) $$

- **Slope Calculation:**
  $$
  m = \frac{5 - 0}{-4 - 2} = \frac{5}{-6} = -\frac{5}{6}
  $$
- **Equation:**
  $$
  y = -\frac{5}{6}x + \frac{5}{3}
  $$

---

If you need further assistance or explanations on any of these equations, feel free to ask!
Here are the equations of the lines passing through each pair of points: 1. $$ y = -5 $$ 2. $$ y = x + 4 $$ 3. $$ y = \frac{1}{4}x - 3 $$ 4. $$ y = -\frac{1}{2}x - \frac{3}{2} $$ 5. $$ x = -5 $$ 6. $$ y = -1 $$ 7. $$ y = \frac{5}{7}x + \frac{10}{7} $$ 8. $$ y = -\frac{1}{2}x $$ 9. $$ y = -\frac{3}{2}x - 4 $$ 10. $$ y = -2x + 1 $$ 11. $$ y = \frac{1}{4}x + 3 $$ 12. $$ y = -\frac{5}{6}x + \frac{5}{3} $$

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