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do you know how to graph `y = -2x - 2` ?

y = -2x - 2 is a linear equation. Ie, a straight line

now use x = 1
if x = 1, then y = ???

you did it right

another point on this line is (1,-4)

yeah because of that underline

IF there wasn't an underline, then it would be a dotted or dashed boundary line

we can use desmos to graph
https://www.desmos.com/calculator

type `y >= -2x-2` to mean \(\Large y \ge -2x-2\)

good

as for the other inequality
y + x ≥ 0 is the same as y ≥ -x (Subtract x from both sides)

you'll need to graph y = -x
then shade above that solid boundary line

notice how in your desmos graph, the shading is above the boundary line
because of the > symbol

do you know how to graph y = -x ?

it's very similar to how we graphed y = -2x-2

if x = 0, then what is y when y = -x ?

so one point on it is (0,0)

then if x = 1, y = ???

yep so we know the two points on it are (0,0) and (1,-1)

now do both graphs at the same time

very good

the final step is to only shade where the two regions overlap one another

yeah pretty much

no problem