Water is running into a bathtub at a constant rate after 2 minutes the tub is filled with 2.5 gallons of water write two equations for this proportional relationship use w for the amount of water and t for time in each case what does the constant of proportionality tell you about the situation

w = 1.25 t

The constant 1.25 denotes the rate of water flowing in the tub per minute.

Step-by-step explanation:

Water is running into a bathtub at a constant rate.

In 2 minutes , 2.5 gallons of water is filled in the tub. We are supposed to find the relation between the amount of water and the time taken and we also have to find the definition of the constant of proportionality.

Let w be the amount of water and t be the time taken in minutes.

The rate at which water is filled in the tub =

                                                                      = 1.25 gallons/minute

The water filled , w = 1.25 t

The constant 1.25 denotes the rate of water flowing in the tub per minute.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

seems like d

step-by-step explanation: