Graph the following lines, be sure to label the point of intersection: y = -x + 2 and y = x - 6 Each line must: 1- Be labeled 2- Formed by three points, one of which is the y-intercept. 3- Extended with arrows.
To graph the lines y = -x + 2 and y = x - 6, let's first find the y-intercepts and plot them.
1. Line y = -x + 2:
The y-intercept occurs when x = 0. Substituting x = 0 into the equation, we find y = -0 + 2 = 2. So the y-intercept is (0, 2).
2. Line y = x - 6:
The y-intercept occurs when x = 0. Substituting x = 0 into the equation, we find y = 0 - 6 = -6. So the y-intercept is (0, -6).
Now, let's find two additional points for each line using different values of x.
1. Line y = -x + 2:
For x = 1, y = -(1) + 2 = 1. So we have the point (1, 1).
For x = -1, y = -(-1) + 2 = 3. So we have the point (-1, 3).
2. Line y = x - 6:
For x = 1, y = (1) - 6 = -5. So we have the point (1, -5).
For x = -1, y = (-1) - 6 = -7. So we have the point (-1, -7).
Now we can plot the lines and label the points:
Line 1 (y = -x + 2):
- y-intercept: (0, 2)
- Additional point: (1, 1) and (-1, 3)
Line 2 (y = x - 6):
- y-intercept: (0, -6)
- Additional point: (1, -5) and (-1, -7)
Here is how the graph would look like:
```
|
7 |- * (-1, 3)
| /
6 |- /
|
5 |- /
| /
4 |-/ *(1, 1)
|
3 |- * (-1, -7)
| /
2 |- /
| /
1 |- *(1, -5)
|
0 |-----------------------
-1 0 1 2 3 4 5 6 7 8 9
```
The point of intersection between the two lines is not labeled, but it is the point (-4, -2).