To represent the number of half-days (4 hours) and full-days (8 hours) that Brad must work to exceed 40 hours of job shadowing, we need to express this in an equation.
Let:
- \( h \) = number of half-days
- \( f \) = number of full-days
The total hours can be expressed as:
\[ 4h + 8f > 40 \]
Simplifying this inequality, we can divide everything by 4:
\[ h + 2f > 10 \]
This inequality indicates that the total number of half-days \( h \) plus twice the number of full-days \( f \) must be greater than 10.
To represent this graphically:
- The line \( h + 2f = 10 \) would serve as the boundary, and we need to shade the area above this line (since we want values greater than 10).
- The graph must account for only non-negative solutions, meaning \( h \geq 0 \) and \( f \geq 0 \).
Now, we can evaluate the options based on these criteria:
- The boundary line (when plotted) should increase, reflecting more hours with more full-days or half-days.
- The feasible region should be in the first quadrant (where both \( h \) and \( f \) are non-negative) and above the line \( h + 2f = 10 \).
Without seeing the actual graphs (W, X, Y, Z), you will need to identify which one has:
- A line representing \( h + 2f = 10 \)
- The area above this line
- Only non-negative values (first quadrant)
If you can provide descriptions or features of those graphs, we can further help identify the correct one.