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Published byClinton Robbins Modified over 8 years ago

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Direct & Inverse Relationships

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Direct Relationships In a direct relationship, as “x” increases “y” increases proportionally. On the graph you see a straight line.

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What is Straight? Logger Pro provides a linear fit that shows the properties of your line in the form of y = mx + b. A perfect line has a correlation of 1.00 Random dots would have a correlation of 0. Our criteria for a line straight enough for the relationship to be called direct is a correlation > 0.95

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Direct Equations Logger Pro provides a linear fit that shows the properties of a direct relationship. From this you can write an equation for the line: Temp= (2.00)time + 12

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Test the Equation T= 2t + 12 From the equation, if 5 minutes have gone by the temperature should be: T = 2(5) + 12 = 22 °C From the graph, a time of 5 minutes matches a temperature of 22 °C. √

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Express the Equation The slope tells us that the temperature is increasing 2.00 °C every minute. “Temperature increases proportionally with time, rising 2.00 °C per minute.”

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Inverse Relationships You can suspect a relationship may be inverse when you see a down sloping curve like this one.

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Inverse Relationship: PROOF Evidence for an inverse relationship comes from calculating the inverse of the “x” axis and plotting it against y. If the relationship IS inverse then this plot will give a straight line ( correlation > 0.95 ).

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Inverse Equation You now have a straight line. PLUG IN: P = 15(1/t) + 0 Note that “b” is approximated as zero. P t = 15 This is the common form of inverse relationships: “xy=k”.

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Test the Inverse From the graph, at 25 sec. the pressure was about 0.6 atm. P t = 15 Using the equation: P (25 sec) =15 P = 15/25 = 0.60 atm √

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Express the Inverse “Pressure decreases over time in an inverse relationship.” BEWARE: “Pressure decreases proportionally (or directly) over time” would be a false statement. It would represent data that looked like this.

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Beware lookalikes! The graph at left looks like the down sloping curve of an inverse relationship. BUT when the inverse of time (1/x) is plotted, the result is NOT a straight line. These data fail the test.

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Review Direct Inverse as “x” increases, “y” increases proportionally y=kx (or y=kx+b) “x” vx. “y” plots as a straight line with correlation > 0.95 as “x” increases, “y” decreases inversely xy = k (or y = k(1/x) + b “1/x” vs. “y” plots as a straight line with correlation > 0.95

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