Alright, let's graph the points [tex]\((-9, 7)\)[/tex] and [tex]\((-3, -2)\)[/tex] on the coordinate plane. Here’s a step-by-step guide on how to do this:
### Step-by-Step:
1. Understanding the coordinate system:
- The horizontal axis is called the x-axis.
- The vertical axis is called the y-axis.
- Points are represented as [tex]\((x, y)\)[/tex], where [tex]\(x\)[/tex] is the horizontal position and [tex]\(y\)[/tex] is the vertical position.
2. Graphing the point [tex]\((-9, 7)\)[/tex]:
- Locate [tex]\(-9\)[/tex] on the x-axis (horizontal axis). Move left from the origin (0,0) to [tex]\(-9\)[/tex].
- From [tex]\(-9\)[/tex] on the x-axis, move vertically up to [tex]\(7\)[/tex] on the y-axis.
- Place a point where this vertical line meets [tex]\(7\)[/tex] on the y-axis.
3. Graphing the point [tex]\((-3, -2)\)[/tex]:
- Locate [tex]\(-3\)[/tex] on the x-axis. Move left from the origin (0,0) to [tex]\(-3\)[/tex].
- From [tex]\(-3\)[/tex] on the x-axis, move vertically down to [tex]\(-2\)[/tex] on the y-axis.
- Place a point where this vertical line meets [tex]\(-2\)[/tex] on the y-axis.
Here are the steps visually represented:
```
y
|
10+
9+
8+
7+ (-9, 7)
6+
5+
4+
3+
2+
1+
0+------------------------------------------------------ x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
1-
2- (-3, -2)
3-
4-
5-
6-
7-
8-
9-
10-
```
With the points correctly plotted on the graph, you can now visually identify their positions. The point [tex]\((-9, 7)\)[/tex] is in the second quadrant, and the point [tex]\((-3, -2)\)[/tex] is in the third quadrant.
