Question

James is making omelettes for his family. He begins with a dozen eggs and each omelette takes 2 eggs. Which graph shows the number of eggs left based on the number of omelettes made?

A. Graph shows Number of omelets on y-axis and number of eggs on x-axis. A line touching the points (0, 0) and (12, 6).

B. Graph shows Number of eggs on y-axis and number of omelets on x-axis. A line touching the points (0, 12) and (6, 0).

C. Graph shows Number of eggs on y-axis and number of omelets on x-axis. A line touching the points (0, 0) and (6, 12).

D. Graph shows Number of omelets on y-axis and number of eggs on x-axis. A line touching the points (0, 6) and (12, 0).

Answer 1

To find which graph accurately represents the relationship between the number of omelettes James can make and the number of eggs left, we need to analyze the situation.

James has 12 eggs, and each omelette requires 2 eggs. Therefore, the number of omelettes (\( o \)) he can make is given by the equation:

\[
o = \frac{12 - e}{2}
\]

where \( e \) is the number of eggs used. Consequently, the number of eggs left after making \( o \) omelettes can be represented as:

\[
e = 12 - 2o
\]

This equation demonstrates that the amount of eggs left decreases as he makes more omelettes.

Now, if we plot this on a graph with the number of omelettes on the x-axis and the number of eggs left on the y-axis, we'll determine key points:

1. When \( o = 0 \) (no omelettes made), \( e = 12 - 2(0) = 12 \). This corresponds to the point (0, 12).
2. When \( o = 6 \) (maximum number of omelettes made), \( e = 12 - 2(6) = 0 \). This corresponds to the point (6, 0).

Now, we check the options:

- **A:** Number of omelettes on y-axis and number of eggs on x-axis, points (0, 0) and (12, 6) — incorrect axes.
- **B:** Number of eggs on y-axis and number of omelettes on x-axis, points (0, 12) and (6, 0) — correct axes and points.
- **C:** Number of eggs on y-axis and number of omelettes on x-axis, points (0, 0) and (6, 12) — incorrect points.
- **D:** Number of omelettes on y-axis and number of eggs on x-axis, points (0, 6) and (12, 0) — incorrect axes and points.

The correct graph is **B**, which shows the number of eggs on the y-axis and the number of omelettes on the x-axis, with points (0, 12) and (6, 0).