A tank of water drains at a constant rate. The table shows the number of gallons of water left in the tank after two different amounts of time. if the time is 10 minutes and theres 450 gallons in the tank and at 30 minutes there's 330 Write a function to model y, the total volume of water remaining in the tank after x minutes of draining.
To model the total volume of water remaining in the tank after x minutes of draining, we can create a linear equation using the given data points.
Let's assume the rate at which the water drains is constant.
We have two data points: (10, 450) and (30, 330).
Using the point-slope form of a linear equation, we can find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is a data point and m is the slope of the line.
Using the first data point (10, 450):
y - 450 = m(x - 10)
Rearranging the equation and solving for m:
y = mx + (450 - 10m) ...........(1)
Using the second data point (30, 330):
330 = m(30) + (450 - 10m)
330 = 30m + 450 - 10m
330 = 20m + 450
20m = -120
m = -6
Substituting the value of m into equation (1):
y = -6x + (450 - 10(-6))
y = -6x + (450 + 60)
y = -6x + 510
Therefore, the function to model y, the total volume of water remaining in the tank after x minutes of draining, is:
y = -6x + 510