Find the coordinates of the vertices of the figure formed by each system of inequalities.
y>=-3
x<=6
y>=x-2
y<=x+5/2
Coordinate for y is -2 and for x its 10.5
To find the coordinates of the vertices of the figure formed by each system of inequalities, we need to first graph the inequalities on a coordinate plane. Then, we can identify the vertices by finding the points where the lines intersect.
Let's start by graphing the first inequality, y >= -3. This is a horizontal line passing through the y-coordinate -3. To plot this, draw a straight line parallel to the x-axis that intersects the y-axis at -3.
Next, let's graph the second inequality, x <= 6. This is a vertical line passing through the x-coordinate 6. Draw a straight line parallel to the y-axis that intersects the x-axis at 6.
Now, let's graph the third inequality, y >= x - 2. This is a line with a slope of 1 passing through the y-intercept -2. Draw a line with a positive slope that intersects the y-axis at -2.
Lastly, let's graph the fourth inequality, y <= x + 5/2. This is a line with a slope of 1 passing through the y-intercept 5/2. Draw a line with a positive slope that intersects the y-axis at 5/2.
Now that we have graphed all the inequalities, let's locate the vertices of the figure. The vertices are the points where the lines intersect.
Starting from the left side of the graph:
1. The first intersection point is at (6, -3) where the horizontal line y = -3 intersects the vertical line x = 6.
2. The second intersection point is at (6, 4.5) where the vertical line x = 6 intersects the line y = x + 5/2.
3. The third intersection point is at (-2, -3) where the horizontal line y = -3 intersects the line y = x - 2.
4. The fourth intersection point is at (-2, -0.5) where the line y = x - 2 intersects the line y = x + 5/2.
Therefore, the coordinates of the vertices of the figure formed by the system of inequalities are:
(6, -3), (6, 4.5), (-2, -3), and (-2, -0.5).