Brandon has a 55-gallon fish tank. He estimates he can drain the tank at an average rate of 11 gallons per minute. In a linear model of this situation, x represents the number of minutes the tank has been draining. Relative to this situation, what does the y-intercept represent?
A: The y-intercept represents the number of minutes it takes to drain the tank.
B: The y-intercept represents the rate at which the tank can be drained.
C: The y-intercept represents the amount of water in the tank after it has been drained.
D: The y-intercept represents the amount of water in the tank before it has been drained
The Actual Answer is The y-intercept represents the amount of water in the tank before it begins Draining.
D: The y-intercept represents the amount of water in the tank before it has been drained.
To determine what the y-intercept represents in this linear model, we need to consider the equation of the line. The equation for a linear model is typically in the form y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, let's assume x represents the number of minutes the tank has been draining, and y represents the amount of water remaining in the tank. Since Brandon estimates he can drain the tank at an average rate of 11 gallons per minute, the slope (m) would be -11 (since the water level decreases over time).
The equation for this linear model can be written as y = -11x + b. The y-intercept (b) represents the value of y when x is equal to 0.
Now, let's analyze the given answer choices:
A: The y-intercept represents the number of minutes it takes to drain the tank.
This is incorrect because the number of minutes it takes to drain the tank is not represented by the y-intercept. The y-intercept only represents the initial amount of water in the tank, not the time it takes to drain it.
B: The y-intercept represents the rate at which the tank can be drained.
This is incorrect because the rate at which the tank can be drained, which is 11 gallons per minute, is reflected in the slope (m) of the equation, not the y-intercept.
C: The y-intercept represents the amount of water in the tank after it has been drained.
This is also incorrect because the y-intercept represents the initial amount of water in the tank, not the amount after it has been drained.
D: The y-intercept represents the amount of water in the tank before it has been drained.
This is the correct answer because the y-intercept (b) of the equation represents the initial amount of water in the tank before any drainage occurs. In this case, it represents the initial amount of water in the 55-gallon fish tank.
Therefore, the correct answer is D: The y-intercept represents the amount of water in the tank before it has been drained.