To determine which number line correctly represents the expression [tex]\(-7 + 8\)[/tex], we need to follow these steps:
1. Identify the starting point: We start at [tex]\(-7\)[/tex] on the number line.
2. Determine the direction and the magnitude of the move: Since we are adding [tex]\(8\)[/tex], we move [tex]\(8\)[/tex] units to the right from [tex]\(-7\)[/tex] on the number line.
Let's break it down:
- Starting at [tex]\(-7\)[/tex], move [tex]\(1\)[/tex] unit to the right: [tex]\(-7 + 1 = -6\)[/tex]
- Move another unit to the right: [tex]\(-6 + 1 = -5\)[/tex]
- Continue moving to the right until you move a total of [tex]\(8\)[/tex] units.
By moving [tex]\(8\)[/tex] units to the right from [tex]\(-7\)[/tex], we arrive at the value [tex]\(1\)[/tex].
Therefore, the correct representation on the number line should show [tex]\(-7\)[/tex] as the starting point and then a movement of [tex]\(8\)[/tex] units to the right, ending up at [tex]\(1\)[/tex]. The correct number line will display a starting point at [tex]\(-7\)[/tex] and an endpoint at [tex]\(1\)[/tex], confirming that the sum of [tex]\(-7\)[/tex] and [tex]\(8\)[/tex] is [tex]\(1\)[/tex].
