Proof: Slope 1

Let's prove the following theorem:

if the following are true:
  • f = (a - b) / (c - d)
  • a = w
  • b = x
  • c = y
  • d = z

then f = (w - x) / (y - z)

Proof:

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Given
1 f = (a - b) / (c - d)
2 a = w
3 b = x
4 c = y
5 d = z
Proof Table
# Claim Reason
1 (a - b) / (c - d) = (w - x) / (y - z) if d = z and c = y and b = x and a = w, then (a - b) / (c - d) = (w - x) / (y - z)
2 f = (w - x) / (y - z) if (a - b) / (c - d) = (w - x) / (y - z) and f = (a - b) / (c - d), then f = (w - x) / (y - z)

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