Represent the fractions 9/7 and -4/7 on a number line.

The given numbers are $\frac{9}{7}$ and $-\frac{4}{7}$.
To represent these on a number line, it's helpful to understand their values relative to integers.
For $\frac{9}{7}$: This is an improper fraction. Convert it to a mixed number: $\frac{9}{7} = 1 \frac{2}{7}$. This means it is greater than 1 but less than 2.
For $-\frac{4}{7}$: This is a negative proper fraction. This means it is greater than -1 but less than 0.

Draw a straight line and mark integer points like -1, 0, 1, 2.

Since $\frac{9}{7} = 1 \frac{2}{7}$, it lies between 1 and 2. Divide the segment between 1 and 2 into 7 equal parts. Count 2 parts from 1 towards 2. This point represents $\frac{9}{7}$.

Since $-\frac{4}{7}$ is between 0 and -1, divide the segment between 0 and -1 into 7 equal parts. Count 4 parts from 0 towards -1. This point represents $-\frac{4}{7}$.

Here is the representation on a number line:

The numbers $\frac{9}{7}$ and $-\frac{4}{7}$ are distinct and are represented at different positions on the number line.