Forecasting Using a Graph
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Often we use some data from the past to make predictions about things that haven’t happened. This works by graphing the data we have, then extending the line into areas where we don’t have data. We usually are given an x value and asked for the y value. The following video will show an example of this kind of forecasting.

Forecast the Value of a Linear Function Using a Graph

Video Source (03:35 mins) | Transcript

Using the line already given, we extend the line so it passes the x values (horizontal) we’re interested in. Draw a vertical line from the x axis to the line to find the point. Trace that point in a horizontal line to the y-axis to find the y value of that point.

Practice Problems

Use this graph to answers questions 1 and 2:
A coordinate plane with a line passing through points at approximately x = 0, y = -3 and x = 0.75, y= -5.
  1. Using the line shown in the graph above, estimate the value of y when \(x=-4\). (
    Solution: Approximately \(7.8\)

    We can’t see the graph of the line where \(x=-4\) so we extend the line to estimate it:
    A line that extends from about (-2, 2.4) to about (2, -8.4). The line has been extended from (-2, 2.4) to the upper left area of the coordinate plane. The extension has been depicted with a dashed line.

    Next, we approximate where \(x=−4\) would fall on the graph. It appears that the y-value is approximately \(7.8\) when \(x=−4\).
    This is the same as the previous image except there is a vertical arrow from the point (-4, 0) on the x-axis to the dashed line. This arrow intersects the dashed line at approximately the point (-4, 7.8).
  2. Using the line shown in the graph above, estimate the value of y when \(x = 6\). (
    Approximately \(-19.2\)

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