Let's break down the translation rule [tex]\( T_{-8,4}(x, y) \)[/tex].
Translation [tex]\( T_{a, b}(x, y) \)[/tex] means that the point [tex]\((x, y)\)[/tex] is translated by moving it [tex]\(a\)[/tex] units horizontally and [tex]\(b\)[/tex] units vertically.
For the translation [tex]\( T_{-8,4}(x, y) \)[/tex]:
1. The [tex]\( -8 \)[/tex] indicates that we move 8 units to the left along the x-axis.
2. The [tex]\( 4 \)[/tex] indicates that we move 4 units up along the y-axis.
To write this rule as an expression, we need to adjust the x and y coordinates accordingly:
- Subtract 8 from the x-coordinate: [tex]\( x \rightarrow x - 8 \)[/tex]
- Add 4 to the y-coordinate: [tex]\( y \rightarrow y + 4 \)[/tex]
Combining these, the rule can be written as:
[tex]\[ (x, y) \rightarrow (x - 8, y + 4) \][/tex]
Therefore, the correct option that describes this translation is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 4) \][/tex]
This matches the third option in the list given above. So, the correct answer is:
[tex]\[ \boxed{(x-8, y+4)} \][/tex]
