Sure, let's represent these given numbers on a number line step by step:
### Step-by-Step Representation
#### Step 1: Understand the values:
- The value of \(\frac{9}{7}\) is approximately \(1.2857\).
- The value of \(\frac{-7}{5}\) is approximately \(-1.4\).
#### Step 2: Draw a number line
Draw a horizontal line, which will act as our number line. Mark the zero point in the center.
```
<----|----|----|----|----|----|----|---->
-3 -2 -1 0 1 2 3
```
#### Step 3: Locate \(\frac{9}{7}\)
The value \(1.2857\) is a bit more than 1 but less than 2. To be precise, it is somewhere between 1 and 1.5. You can represent it as a point on the number line slightly closer to 1.3.
```
<----|----|----|----|----|----|----|---->
-3 -2 -1 0 1 1.3 2 3
\(1.2857\)
```
#### Step 4: Locate \(\frac{-7}{5}\)
The value \(-1.4\) is a bit more than -1 but less than -2. To be precise, it is somewhere between -1.5 and -1. You can represent it as a point on the number line slightly closer to -1.5.
```
<----|----|----|----|----|----|----|---->
-3 -2 -1 -1.5 0 1 2 3
\(-1.4\)
```
#### Final Number Line with both points:
```
<----|----|----|----|----|----|----|---->
-3 -2 -1 -1.5 0 1 1.3 2 3
\( \boxed{-1.4} \) \( \boxed{1.2857} \)
```
In this representation, the positions of [tex]\(\frac{9}{7}\)[/tex] and [tex]\(\frac{-7}{5}\)[/tex] are approximated and plotted correctly on the number line.
