*per*, as in kilometers per hour, dollars per hour, or liters per minute. The first quantity indicates the dependent variable, which is often represented by the variable $y$. The second quantity indicates the independent variable, which is often represented by the variable $x$, or by the variable $t$ if it represents time. The

**, which is the value of $y$ where a graph touches or crosses the $y$-axis, represents the value of the independent variable at the start of the problem, where $x=0$ or $t=0$.**

*y*-interceptThe rate of change is the slope of the line. To determine the slope, choose two points on the graph.

At time $t=0$, Leila is 6 kilometers from the library. This is shown on the graph as $(0, 6)$.

After 2 hours, at $t=2$, her distance from the library is zero kilometers. This is shown on the graph as $(2, 0)$.

The $y$-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 $y$-intercept is 5. This means that there were 5 liters of water already in the bucket at $x=0$ minutes.

The slope represents the number of liters added to the bucket each minute, which is 2 liters per minute.

When $y=20$, the value of $x$ is 7.5. So, the bucket will be full after 7.5 minutes.