Sure, let's proceed step-by-step to determine the ordered pairs and plot them using the given linear equation [tex]\( y = -2x + 4 \)[/tex].
### Step 1: Find the Ordered Pairs
#### For the ordered pair [tex]\((-2, y)\)[/tex]:
1. Substitute [tex]\( x = -2 \)[/tex] into the equation [tex]\( y = -2x + 4 \)[/tex].
2. The equation becomes:
[tex]\[
y = -2(-2) + 4
\][/tex]
3. Simplify the right side:
[tex]\[
y = 4 + 4 = 8
\][/tex]
4. So, the ordered pair is [tex]\( (-2, 8) \)[/tex].
#### For the ordered pair [tex]\((x, 2)\)[/tex]:
1. Substitute [tex]\( y = 2 \)[/tex] into the equation [tex]\( y = -2x + 4 \)[/tex].
2. The equation becomes:
[tex]\[
2 = -2x + 4
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
2 - 4 = -2x \implies -2 = -2x \implies x = 1
\][/tex]
4. So, the ordered pair is [tex]\( (1, 2) \)[/tex].
### Resulting set of ordered pairs:
- [tex]\((-2, 8)\)[/tex]
- [tex]\((1, 2)\)[/tex]
### Step 2: Plot the Ordered Pairs
To plot the points [tex]\((-2, 8)\)[/tex] and [tex]\((1, 2)\)[/tex]:
1. Draw a coordinate plane with the [tex]\(x\)[/tex]-axis (horizontal) and [tex]\(y\)[/tex]-axis (vertical).
2. Locate the point [tex]\((-2, 8)\)[/tex]:
- Move 2 units to the left of the origin along the [tex]\(x\)[/tex]-axis.
- From this position, move 8 units up along the [tex]\(y\)[/tex]-axis.
3. Locate the point [tex]\((1, 2)\)[/tex]:
- Move 1 unit to the right of the origin along the [tex]\(x\)[/tex]-axis.
- From this position, move 2 units up along the [tex]\(y\)[/tex]-axis.
4. Mark these points clearly on the graph.
On a Cartesian coordinate system, the points should be plotted approximately as follows:
```
y
9 |
8 | (-2, 8)
7 |
6 |
5 |
4 |
3 |
2 | (1, 2)
1 |
0 |---|---|---|---|---|---|---|---|---|--- x
-3 -2 -1 0 1 2 3
```
The plotted points [tex]\((-2, 8)\)[/tex] and [tex]\((1, 2)\)[/tex] accurately represent the solutions derived from the linear equation [tex]\( y = -2x + 4 \)[/tex].
