To determine how many eggs James has left based on the number of omelettes made, you can set up a simple equation. James starts with a dozen eggs, which is 12 eggs. Since each omelette requires 2 eggs, the number of eggs left after making \( x \) omelettes can be calculated using the formula:
\[ \text{Eggs left} = 12 - 2x \]
In this equation:
- \( 12 \) is the starting number of eggs.
- \( 2x \) represents the number of eggs used based on the number of omelettes made (where \( x \) is the number of omelettes).
Now, you can derive some values:
- If \( x = 0 \) (no omelettes made), eggs left = \( 12 - 2(0) = 12 \).
- If \( x = 1 \) (1 omelette made), eggs left = \( 12 - 2(1) = 10 \).
- If \( x = 2 \) (2 omelettes made), eggs left = \( 12 - 2(2) = 8 \).
- If \( x = 3 \) (3 omelettes made), eggs left = \( 12 - 2(3) = 6 \).
- If \( x = 4 \) (4 omelettes made), eggs left = \( 12 - 2(4) = 4 \).
- If \( x = 5 \) (5 omelettes made), eggs left = \( 12 - 2(5) = 2 \).
- If \( x = 6 \) (6 omelettes made), eggs left = \( 12 - 2(6) = 0 \).
Beyond 6 omelettes, James would not have enough eggs, and theoretically, you could consider the value to become negative if it continued.
When plotting this on a graph:
- The x-axis represents the number of omelettes made.
- The y-axis represents the number of eggs left.
You'll have a straight line that starts at 12 (when \( x=0 \)) and decreases to 0 (when \( x=6 \)). After \( x=6 \), the value would drop below the y-axis representing negative eggs left.
Make sure to look for a graph with:
- A starting point at (0, 12).
- A slope that descends at a rate of -2 per omelette, leading to the point (6, 0).
This would help you identify the correct graph representing the number of eggs left based on the number of omelettes made.