Question A.5: Suppose the electrical resistance of a metal wire is 5.00 Ω ...

Find the equation of the line describing the resistance R and then substitute the new temperature into it. Two points on the graph of resistance versus temperature, (20.0°C, 5.00 Ω) and (80.0°C, 6.14 Ω), allow computation of the slope:

m=\frac{\Delta R}{\Delta T}=\frac{6.14 \Omega-5.00 \Omega}{80.0^{\circ} C -20.0^{\circ} C }=1.90 \times 10^{-2} \Omega /{ }^{\circ} C                   (1)

Now use the point–slope formulation of a line, with this slope and (20.0°C, 5.00 Ω):

\begin{gathered}R-R_{0}=m\left(T-T_{0}\right)              (2) \\R-5.00 \Omega=\left(1.90 \times 10^{-2} \Omega /{ }^{\circ} C \right)\left(T-20.0^{\circ} C \right)            (3)\end{gathered}

Finally, substitute T 60.0° into (3) and solve for R, getting R = 5.76 Ω.