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
y = 55 - 11 x
or the way I would say it is
depth = 55 - 11 * minutes since start
the y axis intercept is the value of y when x = 0
It is 55.
Now what does that 55 represent?
To determine what the y-intercept represents in this linear model, we can analyze the equation of the line. The equation of a line can be represented as y = mx + c, where y is the dependent variable (in this case, the amount of water in the tank), x is the independent variable (the number of minutes the tank has been draining), m is the slope (the rate at which the tank is draining), and c is the y-intercept.
In this scenario, the line equation would be y = -11x + c, since the tank is being drained at a rate of 11 gallons per minute.
If we substitute x = 0 into the equation, we get y = -11(0) + c = c. This tells us that when x = 0 (the tank has not been draining for any minutes), the value of y (the amount of water in the tank) will be equal to the y-intercept, c.
Therefore, in this specific situation, the y-intercept represents the amount of water in the tank before it has been drained. Hence, the correct answer is D: The y-intercept represents the amount of water in the tank before it has been drained.