To analyze the situation described, let's break down Vicki's volunteering schedule and find a suitable way to represent it graphically.
Let:
- \( x \) = number of 3-hour weekend shifts at the library
- \( y \) = number of 2-hour weekday shifts at the nursing home
Vicki's total volunteering hours for the week can be calculated using the following equation: \[ 3x + 2y > 24 \] This means that the total hours Vicki volunteers must be greater than 24.
To properly represent this equation on a graph:
- The x-axis could represent the number of weekend shifts at the library (\( x \)).
- The y-axis could represent the number of weekday shifts at the nursing home (\( y \)).
The boundary line for the equation \( 3x + 2y = 24 \) can be calculated by setting the equation to find intercepts:
- If \( x = 0 \): \[ 2y = 24 \implies y = 12 \]
- If \( y = 0 \): \[ 3x = 24 \implies x = 8 \]
Thus, the line will intercept the x-axis at (8, 0) and y-axis at (0, 12).
Since we want \( 3x + 2y > 24 \), this means the solution set is above the line.
Now, without the images or graphs provided, I cannot point to the exact graph. However, you should look for a graph where:
- There is a line that passes through points (8, 0) and (0, 12).
- The region above this line (not including the line itself) represents the valid solutions (i.e., the hours Vicki volunteers are more than 24).
If you can describe or share the graphs W, X, Y, and Z, I would be happy to help you identify which one accurately represents this situation!