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MA.912.A.3.11 Modeling Data and Making Predictions with Lines

What You Need To Know...

Write an equation of a line that models a dataset and use the equation or the graph to make predictions.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. All items will include data sets.
  3. Items may require students to describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.
  4. Items may require students to write an equation of a line that models data and/or use the data to make predictions.
  5. In items assessing slope as a rate of change, the slope should be presented as a ratio.
  6. Fill-in response items may require that students provide a slope, the x-coordinate of the x-intercept, the y-coordinate of the y-intercept, or the x-coordinate or y-coordinate of a point of interest.
  7. Items may be set in either real-world or mathematical contexts.

Example One

David is training for a marathon. He writes down the time and distance for each training run and then records the data on a scatter plot.  He has drawn a line of best fit on the scatter plot, as shown below.



Which statement best expresses the meaning of the slope as a rate of change for this line of best fit?

A.  It represents the number of miles he will have to run to finish the marathon.
B.  It represents the average speed, in miles per hour, of his training runs.
C.  It represents the number of hours he will need to finish the marathon.   
D.  It represents the distances, in miles, that he ran while he was training.



Example Two

Joel graphed the line shown on the coordinate plane below.



What is the x-coordinate of the point at which this line intersects the x-axis?

Answer grid.jpg



Example Three

A tank containing water is being drained at a constant rate.  The points on the grid below represent the volume of water remaining in the tank as a function of time.


At what rate, in cubic feet per minute, is the volume of the water changing?



Additional Examples



Fitting a line to Data

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Linear Models

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Modeling a Table of Values

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Modeling a Situation

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Reference Sheet