Draw a line through the point (−2,2)
with a slope of −3
. Draw a line through the point (2,−2)
with a slope of -3
To draw a line with a specific slope passing through a point, we can use the point-slope form of a straight line equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope.
For the first line passing through (-2, 2) with a slope of -3:
y - 2 = -3(x - (-2))
y - 2 = -3(x + 2)
y - 2 = -3x - 6
y = -3x - 4
And for the second line passing through (2, -2) with a slope of -3:
y - (-2) = -3(x - 2)
y + 2 = -3(x - 2)
y + 2 = -3x + 6
y = -3x + 4
Now we can plot these lines on a graph:
Graph:
```
-2 -1 0 1 2 3 4 5 6
+---+---+---+---+---+---+---+---+---+
6 | |
| |
5 | |
| |
4 | |
| |
3 | |
| |
2 | |
| |
1 | |
| X |
0 | |
| |
-1 | X |
| |
-2 | X |
+---+---+---+---+---+---+---+---+---+
-2 -1 0 1 2 3 4 5 6
```
The blue line passing through (-2, 2) with slope -3 is represented by `-3x - 4`, and the orange line passing through (2, -2) with slope -3 is represented by `-3x + 4`.