Linear Equations
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Relationship between shoulder span and height (Investigation)



  • To investigate the relationship between shoulder width and height and create an equation to model it.
  • To practice coming up with an equation based on a given context and changing the subject of the equation.


  • Measuring tape
  • Paper
  • Pen
  • Graphing paper


Work in small groups to complete this investigation.

  1. The span of your shoulders is equivalent to one fourth of your total height.
  2. Let $x$x=span of your shoulders, and $y$y = your total height. Create an equation to represent the span of your shoulders in terms of your total height.
  3. Change the subject of the equation so that your total height is given in terms of your shoulder span.
  4. Discuss with your group if you think the relationship between shoulder span and total height is true.
  5. Measure the distance from shoulder to shoulder and total height of everyone in your group. If you need to, collaborate with other groups so you can have the measurements for at least 5 people.

Record all of the measurements you get on your piece of paper. Create a chart similar to the one shown to keep track.  

Persons Name Shoulder Span Total Height


  1. Analyze the data you collected. Is each person’s total height roughly what you would’ve expected it to be from their shoulder span measurement? Why or why not?
  2. Use the equation solved for total height to fill in the following table of values.  Use Table (a) if you measured in inches, or Table (b) if you measured in centimeters.    
    TABLE A  
    Shoulder Span Total Height
    TABLE B  
    Shoulder Span Total Height
  3. Create a graph of the equation. Put the shoulder span in inches on the x-axis and the total height in inches on the y-axis. Be sure to label the axes and title the graph.
  4. If a person has a shoulder span of 28 inches/71 centimeters what would their height be? Is this reasonable? Why or why not?
  5. Determine the values on the graph that would make sense as measurements of a real person. Explain your reasoning.
  6. Compare and contrast your chosen values with those of another group. Also discuss the method your group used to arrive at that answer.


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