How do you graph x+2y >=-8 on a graphing calculator?

This depends on the capabilities of your calculator, however, converting the equation to a y=... format will work on many (if not all) graphing calculators.

Explanation:

first, lets start making the inequality a bit simpler for the calculator to understand by converting it to a function.

$x + 2 y = - 8$

Then using basic algebra, we can move this to a calculators preferred form by solving for y.

$2 y = - 8 - x$
$y = - \left(\frac{8}{2}\right) - \left(\frac{x}{2}\right)$
$y = - 4 - 0.5 x$

Once you plot this function, you can visualize the range of values where $y \ge - 4 - 0.5 x$
These will be any point on the x,y plane that have a y-coordinate greater than that given by the function, creating a shaded area of infinite points vertically above the line.

For example, (2,1) will be in the shaded area above the line as the value of the function at x=2 (which is y=-5) will be less than the y-value associated with the point (2,1) (which is y=-1).