(a) An equation that represents the relationship between W and T is W = 20T.
(b) The correct statement to represent this relationship is: A. The fish tank is being filled with 20 liters of water per minute.
In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:
y = kx ≡ W = kT
Where:
- y represents the y-variable or W is the amount of water (in liters).
- x represents the x-variable or T is the time (in minutes).
- k is the constant of proportionality.
Part a.
Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 20/1 = 40/2 = 60/3
Constant of proportionality, k = 20.
Therefore, the required linear equation that models the proportional relationship is given by;
y = kx
y = 20x
W = 20T
Part b.
In this context, we can logically deduce that the correct statement is that, the fish tank is being filled with 20 liters of water per minute.
Complete Question:
A fish tank is being filled with water. The graph below shows the relationship between the amount of water W (in liters) in the tank and the time T (in minutes) since the tank started being filled.
(a) Write an equation to represent the relationship between W and T.
(b) Choose the correct statement to represent this relationship.
A. The fish tank is being filled with 20 liters of water per minute.
B. The fish tank is being filled with 1 liter of water per 10 minutes.
C. The fish tank is being filled with 1 liter of water per 20 minutes.
D. The fish tank is being filled with 10 liters of water per minute.