Question

Which point on the graph shows the amount of water in the bucket after 1 second? Hint: Type your answer in the form (x coordinate, y coordinate).

plz answer.

Answer 1

`\displaystyle \left(1,(5)/(12)\right)`

Explanation:

Graphs

The graph shows the amount of water in gallons as a function of time in seconds.

We are required to find the amount of water in the bucked after 1 second. Since the graph does not show an exact location for t=1, we must find the equation of the line.

Two points are clear on the graph: (0,0) (12,5). This gives us the necessary information to find the equation of the line, which has the form:

`w=mt+b`

Where w is the amount of water in the bucket, t is the time, and m and b are two constants to be determined.

Using the point (0,0):

`0=m(0)+b`

It follows that b=0

The equation now takes the form:

`w=mt`

Using the point (12,5):

`5=m(12)`

We find m:

`\displaystyle m=(5)/(12)`

The final equation is:

`\displaystyle w=(5)/(12)\cdot t`

Substituting t=1:

`\displaystyle w(1)=(5)/(12)\cdot (1)=(5)/(12)`

The bucket has 5/12 gallons of water at t=1 second. Expressing the answer as an ordered pair:

`\boxed{\displaystyle \left(1,(5)/(12)\right)}`