Label the vertical axis as the distance traveled and the horizontal axis as the time.
Practice makes perfect
We want to sketch a graph that represents the given situation. To do so, let's start by drawing the axes. We will label the vertical axis as the distance traveled and the horizontal axis as the time.
Before we start drawing, remember that the speed is the ratio of the change in distance to the change in time.
s = Change in Distance/Change in Time
This has the same form as the slope of a line. Cool!
m = Vertical Change/Horizontal Change
In our case, the vertical axis represents the distance traveled, and the horizontal axis represents the time. Then, the slope is the rate between the distance and time. This means that the slope represents the speed. The initial point will be the origin because the distance traveled is zero at the initial time. Now, let's analyze the first part of the situation.
As you snowboard down a hill, you gain speed at a constant rate.
As the speed increases, the distance traveled will also increase. This can be represented as an increasing line segment starting at the origin.
Let's see the next part of the situation.
You come to a steep section of the hill and gain speed a greater constant rate.
As we told before, the distance increases as the speed increases. This time the speed increases faster, so we can sketch the situation with a line segment steeper than the previous line.
Let's see the next situation.
You then slow down at a constant rate until it come to a stop.
Since the speed decreases, the distance traveled in a certain amount of time will also decrease. This can be represented with a decreasing line. After that, we stop our travel, which means that the speed is equal to 0. Then, the distance traveled will be constant in time, which can be sketched as a horizontal line segment.
