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Sagot :
Certainly! Let's go through the steps to plot the given data on a Cartesian plane.
### 1. Understand the Data Points
We are given two lists of values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\(-8, -6, -4, 2, 4, 6\)[/tex]
- [tex]\( y \)[/tex]-values: [tex]\(-8, -6, -4, 2, 4, 6\)[/tex]
Each pair [tex]\((x, y)\)[/tex] from the two lists will be a point on the Cartesian plane:
- [tex]\((-8, -8)\)[/tex]
- [tex]\((-6, -6)\)[/tex]
- [tex]\((-4, -4)\)[/tex]
- [tex]\((2, 2)\)[/tex]
- [tex]\((4, 4)\)[/tex]
- [tex]\((6, 6)\)[/tex]
### 2. Set Up the Cartesian Plane
The Cartesian plane consists of two axes:
- The [tex]\( x \)[/tex]-axis (horizontal)
- The [tex]\( y \)[/tex]-axis (vertical)
Each axis will be marked with the values from the given lists. Given the range of the data, we should have our axes range from at least [tex]\(-10\)[/tex] to [tex]\(10\)[/tex] to accommodate all the points.
### 3. Plot the Points
#### Steps to Plot Each Point:
1. Identify the location on the [tex]\( x \)[/tex]-axis.
2. Identify the corresponding location on the [tex]\( y \)[/tex]-axis.
3. Mark the intersection of these values on the plane to plot the point.
### 4. Draw the Cartesian Plane
#### Example Drawing:
1. Draw the horizontal and vertical lines (axes) and label them as [tex]\( x \)[/tex] and [tex]\( y \)[/tex] respectively.
2. Mark equal intervals along both axes covering the range from [tex]\(-10\)[/tex] to [tex]\(10\)[/tex].
#### Plot and Label Each Point:
- Point [tex]\((-8, -8)\)[/tex]: Go to [tex]\(-8\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(-8\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((-6, -6)\)[/tex]: Go to [tex]\(-6\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(-6\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((-4, -4)\)[/tex]: Go to [tex]\(-4\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(-4\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((2, 2)\)[/tex]: Go to [tex]\(2\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(2\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((4, 4)\)[/tex]: Go to [tex]\(4\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(4\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((6, 6)\)[/tex]: Go to [tex]\(6\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(6\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
### 5. Connect the Points (Optional)
If you observe, the points [tex]\((-8, -8)\)[/tex], [tex]\((-6, -6)\)[/tex], [tex]\((-4, -4)\)[/tex], [tex]\((2, 2)\)[/tex], [tex]\((4, 4)\)[/tex], [tex]\((6, 6)\)[/tex] lie on the line [tex]\( y = x \)[/tex]. Therefore, you can draw a straight line passing through all these points to represent the relationship [tex]\( y = x \)[/tex].
### 6. Final Graph
Your final graph on the Cartesian plane should look like this:
```
y
^
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |-----+-----+-----+-----+-----+-----+-----+-----+-----+-> x
-1|
-2 |
-3 |
-4 |
-5 |
-6 |
-7 |
-8 | *
-9 |
-10|
```
The points at the intersections [tex]\((-8, -8)\)[/tex], [tex]\((-6, -6)\)[/tex], [tex]\((-4, -4)\)[/tex], [tex]\((2, 2)\)[/tex], [tex]\((4, 4)\)[/tex], and [tex]\((6, 6)\)[/tex] should be clearly marked and can be connected via a straight line.
### 1. Understand the Data Points
We are given two lists of values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- [tex]\( x \)[/tex]-values: [tex]\(-8, -6, -4, 2, 4, 6\)[/tex]
- [tex]\( y \)[/tex]-values: [tex]\(-8, -6, -4, 2, 4, 6\)[/tex]
Each pair [tex]\((x, y)\)[/tex] from the two lists will be a point on the Cartesian plane:
- [tex]\((-8, -8)\)[/tex]
- [tex]\((-6, -6)\)[/tex]
- [tex]\((-4, -4)\)[/tex]
- [tex]\((2, 2)\)[/tex]
- [tex]\((4, 4)\)[/tex]
- [tex]\((6, 6)\)[/tex]
### 2. Set Up the Cartesian Plane
The Cartesian plane consists of two axes:
- The [tex]\( x \)[/tex]-axis (horizontal)
- The [tex]\( y \)[/tex]-axis (vertical)
Each axis will be marked with the values from the given lists. Given the range of the data, we should have our axes range from at least [tex]\(-10\)[/tex] to [tex]\(10\)[/tex] to accommodate all the points.
### 3. Plot the Points
#### Steps to Plot Each Point:
1. Identify the location on the [tex]\( x \)[/tex]-axis.
2. Identify the corresponding location on the [tex]\( y \)[/tex]-axis.
3. Mark the intersection of these values on the plane to plot the point.
### 4. Draw the Cartesian Plane
#### Example Drawing:
1. Draw the horizontal and vertical lines (axes) and label them as [tex]\( x \)[/tex] and [tex]\( y \)[/tex] respectively.
2. Mark equal intervals along both axes covering the range from [tex]\(-10\)[/tex] to [tex]\(10\)[/tex].
#### Plot and Label Each Point:
- Point [tex]\((-8, -8)\)[/tex]: Go to [tex]\(-8\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(-8\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((-6, -6)\)[/tex]: Go to [tex]\(-6\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(-6\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((-4, -4)\)[/tex]: Go to [tex]\(-4\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(-4\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((2, 2)\)[/tex]: Go to [tex]\(2\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(2\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((4, 4)\)[/tex]: Go to [tex]\(4\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(4\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
- Point [tex]\((6, 6)\)[/tex]: Go to [tex]\(6\)[/tex] on the [tex]\( x \)[/tex]-axis and [tex]\(6\)[/tex] on the [tex]\( y \)[/tex]-axis, mark the intersection.
### 5. Connect the Points (Optional)
If you observe, the points [tex]\((-8, -8)\)[/tex], [tex]\((-6, -6)\)[/tex], [tex]\((-4, -4)\)[/tex], [tex]\((2, 2)\)[/tex], [tex]\((4, 4)\)[/tex], [tex]\((6, 6)\)[/tex] lie on the line [tex]\( y = x \)[/tex]. Therefore, you can draw a straight line passing through all these points to represent the relationship [tex]\( y = x \)[/tex].
### 6. Final Graph
Your final graph on the Cartesian plane should look like this:
```
y
^
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |-----+-----+-----+-----+-----+-----+-----+-----+-----+-> x
-1|
-2 |
-3 |
-4 |
-5 |
-6 |
-7 |
-8 | *
-9 |
-10|
```
The points at the intersections [tex]\((-8, -8)\)[/tex], [tex]\((-6, -6)\)[/tex], [tex]\((-4, -4)\)[/tex], [tex]\((2, 2)\)[/tex], [tex]\((4, 4)\)[/tex], and [tex]\((6, 6)\)[/tex] should be clearly marked and can be connected via a straight line.
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