Answer :
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]
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]