Let's start by identifying the two numbers you need to plot on the number line: [tex]\(-\frac{7}{5}\)[/tex] and its opposite. The opposite of a number is obtained by changing its sign.
1. Identify the original number and convert it to decimal form:
[tex]\[
-\frac{7}{5} = -1.4
\][/tex]
2. Find the opposite of [tex]\(-1.4\)[/tex]:
- The opposite of [tex]\(-1.4\)[/tex] is [tex]\(1.4\)[/tex].
These are the two numbers you need to plot: [tex]\(-1.4\)[/tex] and [tex]\(1.4\)[/tex].
3. Plotting on the number line:
- First, draw a horizontal line and mark the significant integers: [tex]\(\dots, -3, -2, -1, 0, 1, 2, 3, \dots\)[/tex].
- Locate and mark the decimal points:
- [tex]\(-1.4\)[/tex] will be positioned slightly to the left of [tex]\(-1\)[/tex] but not reaching [tex]\(-2\)[/tex]. It’s closer to [tex]\(-1\)[/tex].
- [tex]\(1.4\)[/tex] will be positioned slightly to the right of [tex]\(1\)[/tex] but not reaching [tex]\(2\)[/tex]. It’s closer to [tex]\(1\)[/tex].
Here is a visual representation of where these points will lie on the number line:
```
<---|---|---|---|---|---|---|---|---|---|---|--->
-3 -2 -1 -0.5 0 0.5 1 2 3
(-1.4) (1.4)
```
- The point [tex]\(-1.4\)[/tex] is marked between [tex]\(-1.5\)[/tex] and [tex]\(-1\)[/tex].
- The point [tex]\(1.4\)[/tex] is marked between [tex]\(1\)[/tex] and [tex]\(1.5\)[/tex].
By carefully placing these points, you have successfully plotted [tex]\(-1.4\)[/tex] and its opposite, [tex]\(1.4\)[/tex], on the number line.
