<u>Given</u>:
The given inequality is ![y \geq-x-3](https://tex.z-dn.net/?f=y%20%5Cgeq-x-3)
We need to determine the graph of the linear inequality.
<u>Slope:</u>
From the given inequality, the slope of the line is given by
![m=-1](https://tex.z-dn.net/?f=m%3D-1)
Thus, the slope of the inequality is -1.
<u>x and y intercept:</u>
The x - intercept can be determined by substituting y = 0 in the equation.
Thus, we have;
![0=-x-3](https://tex.z-dn.net/?f=0%3D-x-3)
![x=-3](https://tex.z-dn.net/?f=x%3D-3)
Thus the coordinates of the x - intercept is (-3,0)
The y - intercept can be determined by substituting x = 0 in the equation.
Thus, we have;
![y =-0-3](https://tex.z-dn.net/?f=y%20%3D-0-3)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
Thus, the coordinate of the y - intercept is (0,-3)
<u>Graphing the inequality:</u>
Let us substitute the coordinate (0,0) to determine the shaded portion.
Thus, we get;
![0\geq -0-3](https://tex.z-dn.net/?f=0%5Cgeq%20-0-3)
![0\geq -3](https://tex.z-dn.net/?f=0%5Cgeq%20-3)
Thus, the coordinate satisfies the inequality.
Hence, the everything to the right of the line is shaded.
Also, the symbol "≥" denotes the solid line.
Thus, On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
Hence Option A is the correct answer.