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Relationships Between Variables

# Relationships Between Variables - X values Y values 2 24 4...

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Relationships Between Variables Scientist usually graph data in order to discover the relationships between variables. Usually the independent variable is graphed along the x-axis while the dependent or responding variable is on the y-axis.

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“Nature does not believe in zigzag patterns”
Graphical Analysis The shape of a graph will allow scientists to know the mathematical relationship between two variables. An equation can be written relating the two variables to each other. You will explore this further in the laboratory.

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Consider the following data and it’s graph: X values Y values 2 1 4 2 8 4 12 6 Sample Data 0 1 2 3 4 5 6 7 0 5 10 15 Series1
Sample Data 0 1 2 3 4 5 6 7 8 0 5 10 15 Series1 Linear (Series1) Since this is a straight line we can describe  this relationship with a linear equation : y = mx + b where m is the slope of the line  and b is the y-intercept

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Consider the following data and it’s graph:

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Unformatted text preview: X values Y values 2 24 4 12 8 6 12 4 Data 2 5 10 15 20 25 30 2 4 8 12 Is this a linear equation? What mathematical relationship will describe this curve? y vs 1/x 10 20 30 0.2 0.4 0.6 Series1 Linear (Series1) • Notice that as one variable increases the other decreases. This is an indication of an inverse relationship. The plot of y vs 1/x (inverse of x) is shown below. • The plot of this inverse relation is a line therefore a linear equation for this graph would be y= k(1/x) where k is the slope of the line. Patterns and Predictions • Extrapolation • Interpolation Graphical analysis • Graph Type Math Relationship • Direct Proportions y=kx • Inverse Proportions y=k(1/x) • Exponential y=kx 2 • Inverse Square y=k(1/x 2 ) • Log y=k(logx)...
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Relationships Between Variables - X values Y values 2 24 4...

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