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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)

1 answer

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.)