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Summary

Direct Variation

• Direct variation means that when the x-values increase by an equal amount, the y-values also increase by an equal amount (which can be different than the increase in the x-values).
  
• The constant factor is called the rate of change.
  

Rate of Change and Slope

• The slope is the steepness of a line on a graph.
  
• In direct variation relationships, the slope of the line always equals the rate of change.
  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mi»m«/mi» «mo»=«/mo» «mfrac» «mi»rise«/mi» «mi»run«/mi» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mi»change«/mi» «mo»§#160;«/mo» «mi»in«/mi» «mo»§#160;«/mo» «mi»y«/mi» «/mrow» «mrow» «mi»change«/mi» «mo»§#160;«/mo» «mi»in«/mi» «mo»§#160;«/mo» «mi»x«/mi» «/mrow» «/mfrac» «/math»
• When two points are known, the slope is calculated using
  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mi»m«/mi» «mo»=«/mo» «mfrac» «mrow» «msub» «mi»y«/mi» «mn»2«/mn» «/msub» «mo»-«/mo» «msub» «mi»y«/mi» «mn»1«/mn» «/msub» «/mrow» «mrow» «msub» «mi»x«/mi» «mn»2«/mn» «/msub» «mo»-«/mo» «msub» «mi»x«/mi» «mn»1«/mn» «/msub» «/mrow» «/mfrac» «/math»
• When a linear relation demonstrates direct variation,
• the graph is a straight line
• the graph contains the ordered pair (0, 0), which is the origin
• the slope, or rate of change, is constant
  

Writing the Equation for a Linear Direct Variation Relationship

• In any direct variation relationship, the equation of the line will be
  y = mx, where m is the slope, or rate of change
  

Using Graphs to Estimate Values

• Interpolation uses known data points to interpret the relationship in between data points. A new data point can be estimated within the range of data collected when using the method of interpolation.
  
• Extrapolation uses data and graphs to predict new data beyond the range of data collected. The line is extended to provide an estimated value beyond the given points when using the method of extrapolation.
  

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