To represent Anna's community service situation with a graph, we need to establish the relationship between the number of hours worked in park beautification and after-school child care and ensure that the total hours meet the requirement of at least 80 hours before graduation.
Let:
- \( x \) be the number of hours Anna spends on park beautification, earning 4 hours each time.
- \( y \) be the number of hours Anna spends on after-school child care, earning 2 hours each time.
The total number of community service hours Anna accrues can be represented as: \[ 4x + 2y \geq 80 \]
To understand how this inequality translates into a graph:
- The line \( 4x + 2y = 80 \) can be derived first to find the boundary (exactly 80 hours).
- We can rewrite this as: \[ 2y = 80 - 4x \] \[ y = 40 - 2x \]
This line will have a y-intercept at 40 (when \( x = 0 \)) and an x-intercept at 20 (when \( y = 0 \)). The area representing hours greater than or equal to 80 would be above this line.
To find the appropriate graph representation:
- Look for a graph where the line \( y = 40 - 2x \) is shown.
- The area above this line should represent the feasible hours (i.e., combinations of \( x \) and \( y \) that satisfy the inequality).
Without seeing the graphs directly, choose the graph that:
- Contains a line with a negative slope passing through points \( (20, 0) \) and \( (0, 40) \), where the area above the line meets the community service condition (greater than or equal to 80 hours).
Choose the graph that best follows this representation. Please consult your available graphs J, K, L, and M and select the correct one based on the criteria above.
3 answers