Find the values of ‘t’ if the points (t, 2t), (2t, 6t) and (3, 8) are collinear.

Let given points A = (t, 2t), B = (2t, 6t) and C = (3, 8) are collinear
$\text{ Slope of }\overline{\mathrm{AB}}=\text{ Slope of }\overline{\mathrm{BC}}$
$\begin{array}{l}\Rightarrow \frac{6\mathrm{t}-2\mathrm{t}}{2\mathrm{t}-\mathrm{t}}=\frac{8-6\mathrm{t}}{3-2\mathrm{t}}\Rightarrow \frac{4\mathrm{t}}{\mathrm{t}}=\frac{8-6\mathrm{t}}{3-2\mathrm{t}}\\ \Rightarrow \frac{4\mathrm{t}}{\mathrm{t}}=\frac{8-6\mathrm{t}}{3-2\mathrm{t}}\\ \Rightarrow 12-8\mathrm{t}=8-6\mathrm{t}\\ \Rightarrow 4=2\mathrm{t}\\ \Rightarrow \mathrm{t}=2\end{array}$