Item 20
A bathtub is draining at a constant rate. After 2 minutes, it holds 28 gallons of water. Three minutes later, it holds 7 gallons of water. Write an equation that represents the number y of gallons of water in the tub after x minutes.
this answer is wrong!!!!!!!!!!!!!!!!!!!😡🤬😱
How did you get 5 in the data point's
2+3=5
To write an equation that represents the number of gallons of water in the tub after x minutes, we can use the given information.
We know that the amount of water in the tub is draining at a constant rate. So, the rate at which the water is draining can be represented by a constant value, let's call it "r".
After 2 minutes, the tub holds 28 gallons of water. So, after 2 minutes, the amount of water that has drained from the tub can be calculated by multiplying the rate with the time: r * 2 = 28. This gives us the equation: 2r = 28.
Similarly, after 5 minutes in total (2 minutes initial time plus 3 minutes later), the tub holds 7 gallons of water. So, after 5 minutes, the amount of water that has drained from the tub is: r * 5 = 7. This gives us the equation: 5r = 7.
Now, to find the equation that represents the number of gallons of water in the tub after x minutes, we need to solve for r in these two equations and then substitute it back into one of the equations.
First, let's solve the equation 2r = 28 for r:
Dividing both sides by 2, we get: r = 14.
Next, let's solve the equation 5r = 7 for r:
Dividing both sides by 5, we get: r = 7/5.
Now, we have two values for r, which means there might be a mistake or inconsistency in the information given. We should double-check the problem statement or clarify the values given for accuracy.
Assuming there was an error and we have found the correct value for r, we can substitute either r = 14 or r = 7/5 back into one of the original equations to get the final equation representing the number of gallons of water in the tub after x minutes.
we have two data points: (2,28) and (5,7)
so, the slope of the line is (7-28)/(5-2) = -7
Using the point-slope form of a line, the function is
y-28 = -7(x-2)
or
y = 42-7x