How are the values of $E_a$ and $A$ obtained from the Arrhenius equation?

According to the Arrhenius equation, which of the following statements is correct?

The temperature dependence of the rate constant $k$ is expressed as $k = A e^{-E_a / RT}$. When a plot between $\log k$ and $1/T$ is plotted,we get the graph as shown. What is the value of the slope in the graph?

For a first order chemical reaction,

The rate constant of a reaction is $2 \times 10^{-3} \ min^{-1}$ at $300 \ K$. By increasing the temperature by $10 \ K$,its value becomes double. Calculate the energy of activation $(E_a)$ and the rate constant at $320 \ K$.

The number of molecules with energy greater than the threshold energy for a reaction increases five-fold by a rise of temperature from $27^{\circ} C$ to $42^{\circ} C$. Its energy of activation in $J \ mol^{-1}$ is.............. (Take $\ln 5 = 1.6094$; $R = 8.314 \ J \ mol^{-1} K^{-1}$)