https://file.aiquickdraw.com/mathbot/file/1728657260424ovq58950.jpg

The question asks to identify the graph of \( p(x) = -2(x + 1) \), which is a transformation of the parent linear function.

### Step-by-step breakdown:

1. **Starting equation**: \( p(x) = -2(x + 1) \)
   
2. **Simplify the equation**:
   \[
   p(x) = -2(x + 1) = -2x - 2
   \]
   The equation is in slope-intercept form \( y = mx + b \), where:
   - Slope (\(m\)) = -2 (this means the line slopes downward at a steepness of 2 units for every 1 unit right)
   - Y-intercept (\(b\)) = -2 (the line crosses the y-axis at -2)

3. **Graph properties**:
   - The line has a negative slope, so it should be slanting downwards from left to right.
   - It should cross the y-axis at \( (0, -2) \).

4. **Look at the options**:
   - The correct graph must match these properties: downward slope and y-intercept of -2.

Based on the image, **Option B** correctly shows these characteristics:
   - It has a negative slope of -2.
   - The y-intercept is -2.

Thus, the correct answer is **Option B**.

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Would you like further clarification on any part of this explanation? Here are some follow-up questions that might help:

1. How do you calculate the slope of a line from an equation?
2. What is the slope-intercept form, and why is it useful?
3. How do transformations (shifts and stretches) affect the graph of a parent function?
4. Why does the negative sign in front of the slope affect the direction of the graph?
5. Can we verify the graph by plotting points?

**Tip**: When determining a graph from an equation, always look for key features like slope and intercepts. These help quickly identify the correct graph.

If p(x) is the linear parent function, which of the following is the graph of p(x) = -2(x + 1)?

This problem involves graphing the linear function p(x) = -2(x + 1) by identifying its slope and y-intercept. The solution explains how to determine the correct graph using key features like the slope (-2) and the y-intercept (-2). Suitable for students in Grades 8-10.

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