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

Answer:

$\displaystyle \left(1,\frac{5}{12}\right)$

Step-by-step 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:

$\displaystyle m=\frac{5}{12}$

The final equation is:

$\displaystyle w=\frac{5}{12}\cdot t$

Substituting t=1:

$\displaystyle w(1)=\frac{5}{12}\cdot (1)=\frac{5}{12}$

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

$\boxed{\displaystyle \left(1,\frac{5}{12}\right)}$