The rate of change is the slope of the line. To determine the slope, choose two points on the graph.
At time , Leila is 6 kilometers from the library. This is shown on the graph as .
After 2 hours, at , her distance from the library is zero kilometers. This is shown on the graph as .
The -intercept is 6. This means that when Leila starts walking and zero hours have passed, she is 6 kilometers from the library.
Leila's rate of change is –3 kilometers per hour. This means she is walking at a speed of 3 kilometers per hour. The rate is negative because her distance from the library is decreasing as she gets closer.
The -intercept is 5. This means that there were 5 liters of water already in the bucket at minutes.
The slope represents the number of liters added to the bucket each minute, which is 2 liters per minute.
When , the value of is 7.5. So, the bucket will be full after 7.5 minutes.