Consider that the amount y in liters of water that flows over a natural waterfall in x seconds is represented by the given equation.
y=500x
We are given a graph that shows the number of liters of water that flow over an artificial waterfall.
We want to find which waterfall has a greater flow. To do so, remember that the rate of change is a ratio used to compare how a variable changes in relation to another variable.
Rate of Change= Change iny/Change in x
This rate of change is also called slope. In our case, the change in y will represent the change in the liters of water and the change in x indicates the change in time.
Rate of Change= Change in Water/Change in Time
Let's start with the rate of change of the artificial waterfall. The change in water will be the difference between 15 000 and 3000 liters. Consider that the initial time is equal to 1 second, so the change in time will be equal to the difference between 5 and 1.
Next, we will calculate the rate of change of the natural waterfall. To do so, remember the equation of a proportional relationship.
y=mx
Here, m represent the constant of proportionality, the slope, and the unit rate. Note that the given equation for the natural waterfall has this form, which means that the slope or rate of change is equal to m=500. Now let's compare the rate of change for each waterfall.
500<3000
This means that the flow over the artificial waterfall is greater than the flow over a natural waterfall.
