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Step-by-Step Explanation:

To determine the correct relationship between the electromotive force of a cell ($E_{\text{cell}}$) and temperature ($T$), we can analyze the fundamental thermodynamic relations governing an electrochemical cell.

1. Relationship between Gibbs Free Energy and Cell EMF:

The standard change in Gibbs free energy ($\Delta G$) for an electrochemical reaction is given by:

$\Delta G=-nF{E}_{\text{cell}}$

where $n$ is the number of moles of electrons transferred and $F$ is Faraday's constant.

2. Fundamental Thermodynamic Relation:

From thermodynamics, the relationship between Gibbs free energy change, enthalpy change ($\Delta H$), and entropy change ($\Delta S$) is:

$\Delta G=\Delta H-T\Delta S$

3. Expressing $E_{\text{cell}}$ as a function of Temperature ($T$):

Substituting $\Delta G=-nF{E}_{\text{cell}}$ into the thermodynamic relation gives:

$-nF{E}_{\text{cell}}=\Delta H-T\Delta S$

Dividing both sides by $-nF$:

$E_{\text{cell}}=-\frac{\Delta H}{nF}+T\left(\frac{\Delta S}{nF}\right)$

Or equivalently, written in slope-intercept form ($y=mx+c$):

$E_{\text{cell}}=\left(\frac{\Delta S}{nF}\right)T-\frac{\Delta H}{nF}$

4. Analyzing the Slope and Graph:

Comparing this to the equation of a straight line $y=mx+c$:

- The y-axis represents $E_{\text{cell}}$.

- The x-axis represents Temperature ($T$).

- The slope ($m$) is given by the temperature coefficient of EMF, $\frac{\partial E_{\text{cell}}}{\partial T}=\frac{\Delta S}{nF}$.

For a standard cell reaction where entropy decreases ($\Delta S<0$), the slope $\frac{\Delta S}{nF}$ is negative. Therefore, as temperature increases, $E_{\text{cell}}$ decreases linearly with a negative slope, starting from a positive y-intercept ($-\frac{\Delta H}{nF}>0$ for an exothermic cell reaction where $\Delta H<0$).

This linear decrease of $E_{\text{cell}}$ with increasing Temperature is correctly represented by the graph showing a straight line with a negative slope, as shown in the selected option.