Video Transcript
Fill in the blank. On a distance–time graph, the
steeper the line through a set of points, the blank the time taken to move one
meter. (A) Less or (B) more.
To answer this question, we need to
work out how the steepness of a line on a distance–time graph relates to the time
taken to travel a meter. To answer this question, let’s draw
a distance–time graph showing two lines with different steepnesses. Here, we have distance on the
vertical axis and we have time on the horizontal axis. We have two lines: a steep pink
line and a shallow blue line. Let’s label our graph so that this
point on the 𝑦-axis corresponds to a distance traveled of one meter. By drawing a horizontal line from
this point, we can see that this corresponds to the final point of both the pink and
blue lines. So, even though they have different
steepnesses, both lines correspond to objects that have traveled a distance of one
meter.
Now, we need to compare the times
taken for each object to travel one meter. Let’s start by drawing a vertical
line from the final point of both the pink and blue lines to the horizontal
axis. Although we don’t have a scale on
our time axis, we can see that the final point of the blue line corresponds to a
greater time than the final point of the pink line. So it took the object corresponding
to the blue line a greater time to travel a distance of one meter than the object
corresponding to the pink line. So the steep pink line represents
an object that took less time to travel one meter than the shallow blue line.
So this tells us that the steeper
the line through a set of points, the less time taken to move one meter. This corresponds to option (A),
which is the correct answer.
