To solve the problem of representing the sum \(-7 + 8\), we first need to calculate the result:
\[ -7 + 8 = 1 \]
Next, we look at the provided number lines to find the correct representation for this sum.
-
Option 1 shows the interval from \(-7\) to \(8\) which represents adding a larger positive number. At the end point of the arrow, it goes to \(8\); however, \(-7 + 8\) equals \(1\), not \(8\).
-
Option 2 shows the interval from \(-7\) to \(1\), which correctly represents \(-7 + 8\) because it includes the closed point at \(-7\) and extends to \(1\).
-
Option 3 shows the interval from \(-7\) to \(-1\), which does not represent \(-7 + 8\).
-
Option 4 shows the interval from \(8\) to \(-7\), which is not relevant for calculating \(-7 + 8\).
Based on this analysis, the correct option that represents \(-7 + 8\) is:
Option 2.