Verified Answer :

  • Start the calculation at \(5\) on the number line.
  • Move \(8\) units to the left because the number being added is negative (\(-8\)).
  • The final position on the number line after moving \(8\) units left from \(5\) is \(-3\).
  • The final result is \(5 + (-8) = \boxed{-3}\).

Explanation

  1. Analyzing the Addition Operation

To solve the expression \(5 + (-8)\) using a number line, we first identify the starting point on the number line, which is \(5\). Adding a negative number is equivalent to subtracting its absolute value. Specifically, adding \(-8\) means we move \(8\) units to the left starting from \(5\).

  1. Calculating the Result on a Number Line

We begin at the point \(5\) on the number line. Moving \(8\) units to the left involves counting down:

  • From \(5\) to \(4\) (1 unit)
  • From \(4\) to \(3\) (2 units)
  • From \(3\) to \(2\) (3 units)
  • From \(2\) to \(1\) (4 units)
  • From \(1\) to \(0\) (5 units)
  • From \(0\) to \(-1\) (6 units)
  • From \(-1\) to \(-2\) (7 units)
  • From \(-2\) to \(-3\) (8 units)

After moving \(8\) units to the left, we reach the coordinate \(-3\). Thus, \(5 + (-8) = -3\).

Examples

Number lines are essential in real-life contexts where values can be positive or negative. For instance, if the temperature is 5 degrees Celsius at noon and it drops by 8 degrees during the night, the temperature at night can be determined using a number line by starting at 5 and moving 8 units into the negative region. This helps visualize debts, altitude changes relative to sea level, or financial balance fluctuations.

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