Question

the graph shows the relationship between the number of liters in a water tank and time. what are the meanings of the initial value and rate of change of the graph? select one number from each group to answer the question. the graph shows the tank began with an amount of 0 / 20 / 30 / 100 / 150 liters of water and was filled at a rate of 0 / 20 / 30 / 100 / 150 liters per minute.

Explanation:

Step1: Identify initial - value

The initial value is the amount of water in the tank at time \(t = 0\). Looking at the graph, when \(t=0\), the number of liters on the \(y\) - axis is \(150\).

Step2: Identify rate - of - change

The rate of change of a linear graph (in the form \(y=mx + b\)) is the slope \(m\). We can take two points on the graph, say \((0,150)\) and \((5,250)\). The slope \(m=\frac{\Delta y}{\Delta x}=\frac{250 - 150}{5-0}=\frac{100}{5}=20\). This means the tank is filled at a rate of 20 liters per minute.

Answer:

The graph shows the tank began with an amount of 150 liters of water and was filled at a rate of 20 liters per minute.