1. The problem asks to use rational numbers to label points on a number line. 2. Rational numbers are numbers that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. 3. For example, points like $-2$, $-1$, $0$, $1$, and $2$ are rational numbers because they can be written as $\frac{-2}{1}$, $\frac{-1}{1}$, $\frac{0}{1}$, $\frac{1}{1}$, and $\frac{2}{1}$ respectively. 4. The opposite of a number $a$ is $-a$. This means if the number is positive, its opposite is negative, and if it is negative, its opposite is positive. 5. For example, the opposite of $-2$ is $2$, the opposite of $1$ is $-1$, and the opposite of $0$ is $0$. 6. To plot points at $-0.5$ and $-1.5$, locate these values on the number line between $-1$ and $0$ for $-0.5$, and between $-2$ and $-1$ for $-1.5$. 7. These points are rational numbers because $-0.5 = \frac{-1}{2}$ and $-1.5 = \frac{-3}{2}$. Final answer: Points labeled with rational numbers include $-2$, $-1$, $0$, $1$, $2$, $-0.5$, and $-1.5$. Their opposites are $2$, $1$, $0$, $-1$, $-2$, $0.5$, and $1.5$ respectively.