Answer: The graph is attached (See explanation).
Step-by-step explanation:
The Slope-Intercept form of the equation of the line is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given inequality:
[tex]x + 2y \geq -6[/tex]
You need to solve for "y":
[tex]2y \geq -x-6\\\\y\geq -\frac{1}{2}x-3[/tex]
You can identify that the line is:
[tex]y= -\frac{1}{2}x-3[/tex]
Which slope and y-intercept are:
[tex]m=-\frac{1}{2}\\\\b=-3[/tex]
To find the x-intercept, substitute [tex]y=0[/tex] into the equation and solve for "x":
[tex]0= -\frac{1}{2}x-3\\\\3= -\frac{1}{2}x\\\\(3)(-2)=x\\\\x=-6[/tex]
Then, you know that the line passes through the points (0,-3) and (-6,0), so you can graph it.
The symbol [tex]\geq[/tex] indicates that the line is solid and you must shade the region above the line.
So, you get the graph attached.
