Forecasting Using a Graph
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In this lesson, you will use graphs to forecast data. You often use some data from the past to make predictions about things that haven’t happened. This works by graphing the data you have then extending the line into areas where you don’t have data. You are usually given an x-value and asked for the y-value.

This video illustrates the lesson material below. Watching the video is optional.

Forecast the Value of a Linear Function Using a Graph

Forecast means to make a prediction about the future. A linear function is just a straight line, so forecasting the value of a linear function is predicting the value of a straight line sometime in the future.

Example 1
Use the line in Figure 1 to forecast what the y-value is when \(x=6\).

\begin{align*} x=6 \rightarrow y = ? \end{align*}

Follow the pattern of this line and draw it further to forecast the y-value when \(x=6\).

\begin{align*} x=6 \rightarrow y = 9.3 \end{align*}

This figure shows how to forecast what the y-value is when x = 6.

Figure 1

Things to Remember

  • Using the line already given, extend the line so you can use it to forecast.
    • Use a ruler or straight edge tool.
    • As needed, use graph paper to get a more accurate graph of functions.
    • Trace vertical and horizontal lines to match the coordinates on the x-axis and y-axis

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 \(7.8\)

    Since you can’t see the graph of the line where \(x = -4\), you will 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, 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 \(x = 6\). (
    Solution: Approximately \(-19.2\)

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