Let's break this problem down step by step.
1. Plot -1 on the number line:
- Starting from 0, move one unit to the left. This position corresponds to -1.
2. Fill in the table for each pair (a, b) and calculate their sum [tex]\(a + b\)[/tex]:
- For [tex]\(a = 1\)[/tex] and [tex]\(b = 2\)[/tex]:
[tex]\[
a + b = 1 + 2 = 3
\][/tex]
Thus, the sum is 3.
- For [tex]\(a = -1\)[/tex] and [tex]\(b = -2\)[/tex]:
[tex]\[
a + b = -1 + (-2) = -1 - 2 = -3
\][/tex]
Thus, [tex]\( R = -3 \)[/tex].
- For [tex]\(a = -4\)[/tex] and [tex]\(b = 1\)[/tex]:
[tex]\[
a + b = -4 + 1 = -3
\][/tex]
Thus, [tex]\( S = -3 \)[/tex].
- For [tex]\(a = -6\)[/tex] and [tex]\(b = -3\)[/tex]:
[tex]\[
a + b = -6 + (-3) = -6 - 3 = -9
\][/tex]
Thus, [tex]\( T = -9 \)[/tex].
3. Complete the table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
a & b & a+b \\
\hline
1 & 2 & 3 \\
\hline
-1 & -2 & R=-3 \\
\hline
-4 & 1 & S=-3 \\
\hline
-6 & -3 & T=-9 \\
\hline
\end{array}
\][/tex]
4. Final answers:
[tex]\[
R = -3
\][/tex]
[tex]\[
S = -3
\][/tex]
[tex]\[
T = -9
\][/tex]
