direct & inverse relationships
DESCRIPTION
Direct & Inverse Relationships. Direct Relationships. In a direct relationship, as “ x ” increases “ y ” increases proportionally. On the graph you see a straight line. What is Straight?. - PowerPoint PPT PresentationTRANSCRIPT
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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 + 12From 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) =15P = 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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ReviewDirect 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