Let's fill in the missing numbers using the rule [tex]\( y = x + 2 \)[/tex]. We need to find the [tex]\( y \)[/tex]-values corresponding to each [tex]\( x \)[/tex]-value. Then, we will write the coordinate pairs [tex]\((x, y)\)[/tex].
1. Point B:
[tex]\( x = 2 \)[/tex]
[tex]\[
y = x + 2 = 2 + 2 = 4
\][/tex]
Coordinate pair: [tex]\((2, 4)\)[/tex]
2. Point C:
[tex]\( x = 3 \)[/tex]
[tex]\[
y = x + 2 = 3 + 2 = 5
\][/tex]
Coordinate pair: [tex]\((3, 5)\)[/tex]
3. Point D:
[tex]\( x = 4 \)[/tex]
[tex]\[
y = x + 2 = 4 + 2 = 6
\][/tex]
Coordinate pair: [tex]\((4, 6)\)[/tex]
4. Point E:
[tex]\( x = 5 \)[/tex]
[tex]\[
y = x + 2 = 5 + 2 = 7
\][/tex]
Coordinate pair: [tex]\((5, 7)\)[/tex]
5. Point F:
[tex]\( x = 6 \)[/tex]
[tex]\[
y = x + 2 = 6 + 2 = 8
\][/tex]
Coordinate pair: [tex]\((6, 8)\)[/tex]
6. Point G:
[tex]\( x = 7 \)[/tex]
[tex]\[
y = x + 2 = 7 + 2 = 9
\][/tex]
Coordinate pair: [tex]\((7, 9)\)[/tex]
Now, let's update the table:
\begin{tabular}{|c|c|c|c|}
\hline
Point & [tex]$x$[/tex] & [tex]$y$[/tex] & [tex]$(x, y)$[/tex] \\
\hline
[tex]$A$[/tex] & 1 & 3 & [tex]$(1, 3)$[/tex] \\
\hline
[tex]$B$[/tex] & 2 & 4 & [tex]$(2, 4)$[/tex] \\
\hline
[tex]$C$[/tex] & 3 & 5 & [tex]$(3, 5)$[/tex] \\
\hline
[tex]$D$[/tex] & 4 & 6 & [tex]$(4, 6)$[/tex] \\
\hline
[tex]$E$[/tex] & 5 & 7 & [tex]$(5, 7)$[/tex] \\
\hline
[tex]$F$[/tex] & 6 & 8 & [tex]$(6, 8)$[/tex] \\
\hline
[tex]$G$[/tex] & 7 & 9 & [tex]$(7, 9)$[/tex] \\
\hline
\end{tabular}
Coordinates to plot:
- [tex]$(1, 3)$[/tex]
- [tex]$(2, 4)$[/tex]
- [tex]$(3, 5)$[/tex]
- [tex]$(4, 6)$[/tex]
- [tex]$(5, 7)$[/tex]
- [tex]$(6, 8)$[/tex]
- [tex]$(7, 9)$[/tex]
Now plot these points on the coordinate plane and draw a line through them. The line will have the equation [tex]\( y = x + 2 \)[/tex], passing through all the given points.
