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 y-intercept has the value of (0, y) which means the x-value is zero. The tank has been draining zero minutes. Now, can you figure out what the y-intercept will be?
To determine the answer to this question, we need to understand what the y-intercept represents in a linear model. In the given situation, the linear model represents the draining rate of the fish tank over time.
The equation of the linear model is represented as y = mx + b, where y is the dependent variable (in this case, the amount of water drained in gallons), x is the independent variable (in this case, the number of minutes), m is the slope of the line (draining rate), and b is the y-intercept.
Since the y-intercept is the value of y when x is equal to 0, it represents the initial condition of the situation. In this case, when x (the number of minutes) is 0, it means no time has passed, and thus the tank has not been drained. Therefore, the correct answer is:
D: The y-intercept represents the amount of water in the tank before it has been drained.