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Why does 0 - (-3) become 0+30 + 3 in the slope calculation?

Subtracting a negative number is mathematically equivalent to adding its positive counterpart. In the slope calculation, the expression 0−(−3)0 - (-3) represents the difference between the y-coordinates. Applying the rule a−(−b)=a+ba - (-b) = a + b, it simplifies to 0+30 + 3, which equals 3.

Conditions

  • The arithmetic operation involves subtracting a negative number.
  • The context is evaluating the numerator of the slope formula y2−y1y_2 - y_1.
  • The values are y2=0y_2 = 0 and y1=−3y_1 = -3.

Reasoning, step by step

  1. Identify the expression to be evaluated: 0−(−3)0 - (-3).
  2. Recall the arithmetic rule for subtracting negative numbers: subtracting a negative is the same as adding a positive.
  3. Apply the rule to rewrite the expression as 0+30 + 3.
  4. Calculate the final sum: 3.

Example

The video states: "Zero minus negative three, that’s the same as zero plus three." The board explicitly rewrites 0−(−3)0-(-3) as 0+(+3)0+(+3).

Common misconceptions

  • Keeping the minus sign and treating it as 0−3=−30 - 3 = -3.
  • Confusing the rule for subtracting negatives with the rule for multiplying negatives.
  • Thinking that the sign of the result depends only on the first number.

Watch the explanation

3:24 – 3:41Watch this moment ↗

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Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.