The rate constant is only constant for a fixed temperature. It increases exponentially as the temperature increases. Arrhenius came up with the following relationship:
k= A exp -Ea/RT
This is often shown in logarithmic form so that it is the form of y=mx + c form and a graph of lnk against 1/T can be plotted which has a slope of -Ea/R.
Look at page 123 in The Chemistry Course Companion (Geoff Neuss) and the following Chemguide link is useful.
The Arrhenius Equation
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