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.

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.