To solve the problem, we need to use the rule given to find the missing [tex]\(y\)[/tex] values and then determine the coordinate pairs [tex]\((x, y)\)[/tex] for each point. The rule provided is:
[tex]\[ y = x + 2 \][/tex]
We will apply this rule to each [tex]\(x\)[/tex] value to find the corresponding [tex]\(y\)[/tex] value.
1. Point A:
[tex]\[ x_A = 1 \][/tex]
[tex]\[ y_A = 1 + 2 = 3 \][/tex]
[tex]\[ (x_A, y_A) = (1, 3) \][/tex]
2. Point B:
[tex]\[ x_B = 2 \][/tex]
[tex]\[ y_B = 2 + 2 = 4 \][/tex]
[tex]\[ (x_B, y_B) = (2, 4) \][/tex]
3. Point C:
[tex]\[ x_C = 3 \][/tex]
[tex]\[ y_C = 3 + 2 = 5 \][/tex]
[tex]\[ (x_C, y_C) = (3, 5) \][/tex]
4. Point D:
[tex]\[ x_D = 4 \][/tex]
[tex]\[ y_D = 4 + 2 = 6 \][/tex]
[tex]\[ (x_D, y_D) = (4, 6) \][/tex]
5. Point E:
[tex]\[ x_E = 5 \][/tex]
[tex]\[ y_E = 5 + 2 = 7 \][/tex]
[tex]\[ (x_E, y_E) = (5, 7) \][/tex]
6. Point F:
[tex]\[ x_F = 6 \][/tex]
[tex]\[ y_F = 6 + 2 = 8 \][/tex]
[tex]\[ (x_F, y_F) = (6, 8) \][/tex]
7. Point G:
[tex]\[ x_G = 7 \][/tex]
[tex]\[ y_G = 7 + 2 = 9 \][/tex]
[tex]\[ (x_G, y_G) = (7, 9) \][/tex]
Now, let's update the coordinate pairs in the table:
[tex]\[
\begin{tabular}{|c|c|c|l|}
\hline Point & $x$ & $y$ & $(x, y)$ \\
\hline A & 1 & 3 & $(1, 3)$ \\
\hline B & 2 & 4 & $(2, 4)$ \\
\hline C & 3 & 5 & $(3, 5)$ \\
\hline D & 4 & 6 & $(4, 6)$ \\
\hline E & 5 & 7 & $(5, 7)$ \\
\hline F & 6 & 8 & $(6, 8)$ \\
\hline G & 7 & 9 & $(7, 9)$ \\
\hline
\end{tabular}
\][/tex]
To plot these points on a coordinate plane:
1. Point A: [tex]\((1, 3)\)[/tex]
2. Point B: [tex]\((2, 4)\)[/tex]
3. Point C: [tex]\((3, 5)\)[/tex]
4. Point D: [tex]\((4, 6)\)[/tex]
5. Point E: [tex]\((5, 7)\)[/tex]
6. Point F: [tex]\((6, 8)\)[/tex]
7. Point G: [tex]\((7, 9)\)[/tex]
After plotting these points, draw a straight line through all the points. This line will represent the linear relationship given by the equation [tex]\(y = x + 2\)[/tex]. The points will lie perfectly on this line, confirming the consistency of the rule.
