Let’s analyze each equation and find the correct slope and y-intercept.
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Equation: \( y = 4x + \frac{1}{2} \)
- Slope = 4
- Y-intercept = \( \left(0, \frac{1}{2}\right) \)
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Equation: \( y = -4x + \frac{1}{2} \)
- Slope = -4
- Y-intercept = \( \left(0, \frac{1}{2}\right) \)
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Equation: \( y = \frac{1}{2}x - 4 \)
- Slope = \( \frac{1}{2} \)
- Y-intercept = \( \left(0, -4\right) \)
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Equation: \( y = \frac{1}{2}x + 4 \)
- Slope = \( \frac{1}{2} \)
- Y-intercept = \( \left(0, 4\right) \)
Now, let's match them:
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For \( y = 4x + \frac{1}{2} \):
- Slope: 4
- Y-intercept: \( \left(0, \frac{1}{2}\right) \)
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For \( y = -4x + \frac{1}{2} \):
- Slope: -4
- Y-intercept: \( \left(0, \frac{1}{2}\right) \)
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For \( y = \frac{1}{2}x - 4 \):
- Slope: \( \frac{1}{2} \)
- Y-intercept: \( \left(0, -4\right) \)
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For \( y = \frac{1}{2}x + 4 \):
- Slope: \( \frac{1}{2} \)
- Y-intercept: \( \left(0, 4\right) \)
Summary of Matches:
- \( y = 4x + \frac{1}{2} \) → Slope: 4, Y-intercept: \( \left(0, \frac{1}{2}\right) \)
- \( y = -4x + \frac{1}{2} \) → Slope: -4, Y-intercept: \( \left(0, \frac{1}{2}\right) \)
- \( y = \frac{1}{2}x - 4 \) → Slope: \( \frac{1}{2} \), Y-intercept: \( \left(0, -4\right) \)
- \( y = \frac{1}{2}x + 4 \) → 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.)