Question about parametric equations

Question

This is a question from MIT 18.01 single variable calculus on parametric equations:

I have the answers, but I don't quite understand it, especially the equation circled in pink. What does it mean? Moreover, I don't get how it equates to $\theta = \frac{\pi}{2} - \frac{\pi}{6}t$. I believe it might be a typo.

Answer 1

$\theta$ is a linear function of $t$. So to derive its equation, think of how to find the equation of a line knowing its value at two places. You know that $\theta=\frac\pi2$ when $t=0$ and that $\theta=\frac\pi3$ when $t=1$. So calculate rise over run: $$ \frac{\theta-\theta_0}{t-t_0}=\frac{\theta_1-\theta_0}{t_1-t_0}. $$ and then plug in: $$\frac{\theta - \frac\pi2}{t-0}=\frac{\frac\pi3-\frac\pi2}{1-0} $$

Answer 2

The hand starts at an angle of $\theta = \frac{\pi}{2}$ (12 o clock). It then moves clockwise (hence the minus sign) and traverses one twelfth of full rotation in one hour, which is a unit of $1$ for $t$. And a full rotation is $2\pi$, so $2\pi/12=\pi/6$.