https://file.aiquickdraw.com/mathbot/file/1730001454988fr1w8vjp.jpg

To determine the algebraic rule for this transformation, let’s analyze how each point on the shape has changed.

### Step-by-Step Solution:
1. **Identify the Coordinates of Each Point:**
   - For the original shape (left), let’s label each point:
     - \( G \) is at \( (-4, 4) \)
     - \( H \) is at \( (-2, 4) \)
     - \( J \) is at \( (-1, 1) \)
     - \( K \) is at \( (-3, 1) \)

   - For the transformed shape (right), we can label each corresponding point:
     - \( G' \) is at \( (2, 4) \)
     - \( H' \) is at \( (4, 4) \)
     - \( J' \) is at \( (5, 1) \)
     - \( K' \) is at \( (3, 1) \)

2. **Determine the Transformation Type:**
   - The transformation from the original shape to the image appears to shift the points to the right without changing the y-coordinates, indicating a **horizontal translation**.

3. **Calculate the Translation Distance:**
   - Comparing points \( G \) and \( G' \): the x-coordinate moves from \( -4 \) to \( 2 \), an increase of \( 6 \).
   - This shift is consistent across all points: each x-coordinate has increased by \( 6 \).

4. **Algebraic Rule for the Transformation:**
   - Since only the x-coordinates have changed (increased by 6), the transformation rule is:
     \[
     (x, y) \rightarrow (x + 6, y)
     \]

### Final Answer:
The algebraic rule that represents this transformation is:
\[
(x, y) \rightarrow (x + 6, y)
\]

Would you like further clarification on any part of this solution?

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### Further Questions to Explore:
1. How would the rule change if the shape were translated downward by 3 units?
2. Can you identify a different transformation that would map the original figure to the same points without using translation?
3. What algebraic rule would represent a reflection of the original shape over the y-axis?
4. How would the transformation rule change if the shape were rotated 90 degrees clockwise about the origin?
5. What would be the new coordinates if the shape were translated by \((x - 2, y + 5)\)?

### Tip:
When determining transformation rules, always check both x- and y-coordinates for changes to identify if it's a translation, reflection, or rotation.

Which algebraic rule represents the transformation shown on the grid?

Explore how to find the algebraic rule for a transformation on a coordinate grid, focusing on translation in coordinate geometry. This step-by-step solution demonstrates a horizontal translation rule for mapping a shape, suitable for Grade 8 math students.

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