Answer: The graph is attached (See explanation).
Step-by-step explanation:
The Slope-Intercept form of the equation of the line is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where "m" is the slope and "b" is the y-intercept.
Given inequality:
![x + 2y \geq -6](https://tex.z-dn.net/?f=x%20%2B%202y%20%5Cgeq%20%20-6)
You need to solve for "y":
![2y \geq -x-6\\\\y\geq -\frac{1}{2}x-3](https://tex.z-dn.net/?f=2y%20%5Cgeq%20-x-6%5C%5C%5C%5Cy%5Cgeq%20-%5Cfrac%7B1%7D%7B2%7Dx-3)
You can identify that the line is:
![y= -\frac{1}{2}x-3](https://tex.z-dn.net/?f=y%3D%20-%5Cfrac%7B1%7D%7B2%7Dx-3)
Which slope and y-intercept are:
![m=-\frac{1}{2}\\\\b=-3](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Cb%3D-3)
To find the x-intercept, substitute
into the equation and solve for "x":
![0= -\frac{1}{2}x-3\\\\3= -\frac{1}{2}x\\\\(3)(-2)=x\\\\x=-6](https://tex.z-dn.net/?f=0%3D%20-%5Cfrac%7B1%7D%7B2%7Dx-3%5C%5C%5C%5C3%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%5C%5C%5C%5C%283%29%28-2%29%3Dx%5C%5C%5C%5Cx%3D-6)
Then, you know that the line passes through the points (0,-3) and (-6,0), so you can graph it.
The symbol
indicates that the line is solid and you must shade the region above the line.
So, you get the graph attached.