To represent Anna's community service hours graphically, we need to create a graph where the x-axis represents the number of times she serves in park beautification (let's call this \( x \)) and the y-axis represents the number of times she serves in after-school child care (let's call this \( y \)).
Each service with park beautification earns her 4 hours, so the contribution of park beautification to her total hours can be represented by \( 4x \). Each service with after-school child care earns her 2 hours, so the contribution of after-school child care can be represented by \( 2y \).
The total hours of community service Anna needs to complete is 80 hours. Therefore, the equation we need to represent is:
\[ 4x + 2y \geq 80 \]
We can simplify this inequality to:
\[ 2x + y \geq 40 \]
Interpreting the graph:
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The line \( 2x + y = 40 \) will have intercepts that can be calculated:
- If \( x = 0 \) (no park beautification), then \( y = 40 \) (20 after-school child care sessions).
- If \( y = 0 \) (no after-school child care), then \( x = 20 \) (5 park beautification sessions).
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The area above this line will represent the combinations of park beautification and after-school child care that satisfy Anna's requirement of at least 80 hours of community service.
Now, if you have multiple graphs (J, K, L, M) to choose from, look for a graph that has:
- A line with a downward slope intersecting the x-axis at 20 and y-axis at 40.
- A shaded area above the line, indicating the hours are greater than or equal to 80.
Once you identify a graph that meets this criteria, you will have found the correct representation of Anna's community service requirement.