Exit Ticket: At noon, a tank has a water depth of 9 in. After 3 hours, the depth was 8 inches. At 6pm, the depth was 7 inches. What is the initial value for the function? help will be appreciated.

Step-by-step explanation:

The  straight line equation is:

y = m*x  + b     Where m is the slope of the line and b the intercept with   y-axis, in our case y is the depth of the tank and x (time in lapsus of 3 hours).

The slope m  =  ( y₂ -  y₁ ) / (x₂ - x₁)

We have point  A ( 3 , 8 )  and point  B ( 6 , 7 )

m  = ( 6 - 3 ) / (7 - 8 )  m = -3

We see that  each 3 hours time-depth decreases  1 in.

Then   to find the depth at the beginning of x-axis

At  noon     12   tank was  9 inches, three hours before at 9 in the morning the depth was 10 inches and:

9  in the morning   10

6  in the morning   11

3  in the midnight   12

12 in the night         13

Then 13 is the intercept with y-axis

then the equation is:

h = - 3*x + 13

Note x is time in lapsus  of 3 hours

linear pair postulates