Vertices of the Triangle formed by the Given Lines

To determine the vertices of the triangle formed by the lines x=0, y=2, and x+y=-4, we can follow these steps:

- Plot the lines on a coordinate plane.
- Identify the points of intersection between the lines.
- These points of intersection will be the vertices of the triangle.

Plotting the Lines:
To plot the lines, we need to determine their slopes and y-intercepts.

The line x=0 is a vertical line passing through the point (0,0). It is parallel to the y-axis.

The line y=2 is a horizontal line passing through the point (0,2). It is parallel to the x-axis.

The line x+y=-4 can be rewritten in slope-intercept form as y=-x-4. This line has a slope of -1 and a y-intercept of -4.

Identifying the Points of Intersection:
To find the points of intersection, we can set up pairs of equations and solve them simultaneously.

1. x=0 and y=2:
Since x=0 and y=2 are already given, the point of intersection is (0,2).

2. x=0 and y=-x-4:
Substituting x=0 into the equation y=-x-4, we get y=-0-4, which gives y=-4. The point of intersection is (0,-4).

3. y=2 and y=-x-4:
Setting the two equations equal to each other, we get 2=-x-4. Solving for x, we have x=-6. Substituting this value into either equation, we find y=2. The point of intersection is (-6,2).

Vertices of the Triangle:
The points of intersection we found are (0,2), (0,-4), and (-6,2). These are the vertices of the triangle formed by the lines x=0, y=2, and x+y=-4.

Conclusion:
The vertices of the triangle formed by the lines x=0, y=2, and x+y=-4 are (0,2), (0,-4), and (-6,2). By plotting the lines and finding their points of intersection, we can visually determine the vertices of the triangle.