Question

Match each equation with the correct slope and y-intercept


y = 4x + 1/2

Slope: 1/2 y-intercept: (0, - 4)

y = - 4x + 1/2

Slope: -4 y-intercept: (0, 1/2)

y = 1/2 * x - 4

1/2 Slope: y-intercept: (0, 4)

y = 1/2 * x + 4

Slope: 4 yintercept: (0, 1/2)

Answer 1

Let’s analyze each equation and find the correct slope and y-intercept.

1. **Equation: \( y = 4x + \frac{1}{2} \)**
- Slope = 4
- Y-intercept = \( \left(0, \frac{1}{2}\right) \)

2. **Equation: \( y = -4x + \frac{1}{2} \)**
- Slope = -4
- Y-intercept = \( \left(0, \frac{1}{2}\right) \)

3. **Equation: \( y = \frac{1}{2}x - 4 \)**
- Slope = \( \frac{1}{2} \)
- Y-intercept = \( \left(0, -4\right) \)

4. **Equation: \( y = \frac{1}{2}x + 4 \)**
- Slope = \( \frac{1}{2} \)
- Y-intercept = \( \left(0, 4\right) \)

Now, let's match them:

- **For \( y = 4x + \frac{1}{2} \)**:
- Slope: 4
- Y-intercept: \( \left(0, \frac{1}{2}\right) \)

- **For \( y = -4x + \frac{1}{2} \)**:
- Slope: -4
- Y-intercept: \( \left(0, \frac{1}{2}\right) \)

- **For \( y = \frac{1}{2}x - 4 \)**:
- Slope: \( \frac{1}{2} \)
- Y-intercept: \( \left(0, -4\right) \)

- **For \( y = \frac{1}{2}x + 4 \)**:
- Slope: \( \frac{1}{2} \)
- Y-intercept: \( \left(0, 4\right) \)

### Summary of Matches:
1. \( y = 4x + \frac{1}{2} \) → Slope: 4, Y-intercept: \( \left(0, \frac{1}{2}\right) \)
2. \( y = -4x + \frac{1}{2} \) → Slope: -4, Y-intercept: \( \left(0, \frac{1}{2}\right) \)
3. \( y = \frac{1}{2}x - 4 \) → Slope: \( \frac{1}{2} \), Y-intercept: \( \left(0, -4\right) \)
4. \( y = \frac{1}{2}x + 4 \) → Slope: \( \frac{1}{2} \), Y-intercept: \( \left(0, 4\right) \)

(Note: The matches can have some repetitions in y-intercept values, which have been addressed.)