Extrapolation & Interpolation with Line Graphs

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  • 0:05 Line Graphs
  • 0:51 Points to Line
  • 1:21 Interpolation
  • 2:15 Extrapolation
  • 2:59 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you should be able to interpolate and extrapolate a line graph based on just a few points. You will be able to provide data points that haven't been given to you.

Line Graphs

In this video lesson, we talk about line graphs. What do you think these types of graphs look like based on the name? If you guessed they look like a line, then you are correct! Line graphs are graphs that have a line connecting the data points. If the data points line up nicely, then we get a straight line graph. If the points don't line up nicely, then we get a zigzagged line. For this video lesson, we will consider the case when our points line up nicely to make a straight line.

Do you remember how we plot points on a graph? We plot the points one at a time. Our points are in (x, y) form and we look for the point on the graph that corresponds to that point. So, the point (1, 2) will be located at the intersection where x = 1 and y = 2.

Points to Line

Say, for instance, we charted the growth of a cherry tree from the moment it starts growing for a period of three weeks. We get these data points:

  • (0, 0)
  • (7, 3.5)
  • (14, 7)

We measured the tree once a week. The x number represents days and the y number represents the growth of the cherry tree in inches.

Plotting these points, we get this kind of line graph:

Graph for cherry tree growth data
interpolate and extrapolate graph

The points line up nicely to form a straight line.


Because we have a nice straight line, we can interpolate our data. What does this mean? It means we can make educated guesses about what happens in the spaces between our data points. Do you see how we only have three points that are spaced out from each other? Because our line is a nice straight line, we can make fairly accurate guesses about how our cherry tree grows on the days that we didn't measure its height.

For example, look at day two. According to our line graph, what can we say about the growth of the cherry on day two? It looks like the line passes through the point (2, 1), so we can say that our cherry tree has grown to a height of one inch on day two. What about day ten? It looks like the cherry tree is five inches tall on day ten as it passes through the point (10, 5).

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