Max puts a stopper in the bathtub and turns on the faucet at time t=0.after 5 minutes there are 11 gallons of water in the tub and after 10 minutes there are 22 gallons in the tub. write an equation that relates the number of gallons g to t minutes. dose the relationship represent a linear function? explain

Step-by-step explanation:

I've seen this before... I'm assuming your questions are the following:

A) How many gallons are there in the tub after 5 minutes?

To answer this, you need to know how many additional gallons of water there will be after 5 minutes. So if for every minute, a 1/2 gallon is added, then after 5 minutes, there will be how many gallons added?  

Then, add the amount of gallons that were initially in the tub in order to get the total amount of water after 5 minutes.  

You should get 8 1/2 gallons.

B) Write an equation using y as gallons and x as minutes.  

For this problem, it is useful to utilize the equation of a line:

y=mx + b

Where m is the rate of change (slope), and b is where the water level is at when time begins "begins" (y-intercept).

We know the water level increases by 1/2 gallon every minute. So that is our m value. We also know that the tube starts at 6 gallons, so that is our b value. Therefore, we get:

Y = (1/2)x +6

C) Using part b, find how many minutes have passed for there to be exactly 23 3/4 gallons.

For this, we use our equation and solve for the number of minutes (x). This means we want to isolate x out get it all by itself. First, we subtract 6 from both sides:

y-6 = (1/2)x

Then, we need to get rid of the 1/2. So we multiply both sides by 2:

2(y-6) = x

Now, we plug in 23 3/4 for y and solve.

2(23 3/4 - 6) = x

2(17 3/4) = x

35 1/2 = x

So after 35 1/2 minutes, there will be 23 3/4 gallons in the tub.

Does that helpI've seen this before... I'm assuming your questions are the following:

A) How many gallons are there in the tub after 5 minutes?

To answer this, you need to know how many additional gallons of water there will be after 5 minutes. So if for every minute, a 1/2 gallon is added, then after 5 minutes, there will be how many gallons added?  

Then, add the amount of gallons that were initially in the tub in order to get the total amount of water after 5 minutes.  

You should get 8 1/2 gallons.

B) Write an equation using y as gallons and x as minutes.  

For this problem, it is useful to utilize the equation of a line:

y=mx + b

Where m is the rate of change (slope), and b is where the water level is at when time begins "begins" (y-intercept).

We know the water level increases by 1/2 gallon every minute. So that is our m value. We also know that the tube starts at 6 gallons, so that is our b value. Therefore, we get:

Y = (1/2)x +6

C) Using part b, find how many minutes have passed for there to be exactly 23 3/4 gallons.

For this, we use our equation and solve for the number of minutes (x). This means we want to isolate x out get it all by itself. First, we subtract 6 from both sides:

y-6 = (1/2)x

Then, we need to get rid of the 1/2. So we multiply both sides by 2:

2(y-6) = x

Now, we plug in 23 3/4 for y and solve.

2(23 3/4 - 6) = x

2(17 3/4) = x

35 1/2 = x

So after 35 1/2 minutes, there will be 23 3/4 gallons in the tub.

Does that help

 g = 2.2t; The equation represents a linear function because the equation is in the form y = mx.

Step-by-step explanation: I did the test! yw :)

true !

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answer: 0.64

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