Question

Bottle X contains 1 L of water, while bottle Y, which has the same capacity as X, is empty. Water is poured from bottle X to Y. The plot of the quantity of water in Y as a function of the quantity of water in X is:

• A. an exponential function
• B. straight line with a slope of 0
• C. straight line with a slope of 1
• D. straight line with a slope of -1

Hint:

In problems involving a constant transfer between two quantities, the relationship is typically linear, and the slope reflects the rate of change between the variables.

Answer 1

The Correct Option is D

Step 1: Understanding the situation.
Since the water is being transferred from bottle X (with 1 L of water) to bottle Y, the amount of water in bottle Y increases as the amount in bottle X decreases. The total quantity of water in both bottles remains constant (1 L). The relationship between the water in X and Y is linear, as the transfer happens at a constant rate.

Step 2: Analyzing the options.
- (A) an exponential function: This is incorrect as the transfer is happening at a constant rate, not an increasing or decreasing rate.
- (B) straight line with a slope of 0: This is incorrect because the water in Y changes as the water in X changes.
- (C) straight line with a slope of 1: This would indicate that the amount of water in Y increases at the same rate as it decreases in X, but the slope is actually negative.
- (D) straight line with a slope of -1: Correct — As water moves from X to Y, for every unit decrease in X, there is an equal unit increase in Y, resulting in a slope of -1.

Step 3: Conclusion.
The correct answer is (D) because the plot represents a straight line with a slope of -1.