Answer:
[tex]\displaystyle \left(1,\frac{5}{12}\right)[/tex]
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:
[tex]w=mt+b[/tex]
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):
[tex]0=m(0)+b[/tex]
It follows that b=0
The equation now takes the form:
[tex]w=mt[/tex]
Using the point (12,5):
[tex]5=m(12)[/tex]
We find m:
[tex]\displaystyle m=\frac{5}{12}[/tex]
The final equation is:
[tex]\displaystyle w=\frac{5}{12}\cdot t[/tex]
Substituting t=1:
[tex]\displaystyle w(1)=\frac{5}{12}\cdot (1)=\frac{5}{12}[/tex]
The bucket has 5/12 gallons of water at t=1 second. Expressing the answer as an ordered pair:
[tex]\boxed{\displaystyle \left(1,\frac{5}{12}\right)}[/tex]
