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do you know how to graph `y = -2x - 2` ?
y = -2x - 2 is a linear equation. Ie, a straight line
if x = 0 for instance, then y is... y = -2x - 2 y = -2*0 - 2 ... replace x with 0 y = 0 - 2 y = -2 so we have the point (0,-2). Do you see how I got this?
now use x = 1 if x = 1, then y = ???
you did it right
another point on this line is (1,-4)
plot the two points (0,-2) and (1,-4). Draw a straight line through them since we have this sign ≥, which has a line under the ">", we will make this boundary line solid
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 \(\Large y \ge -2x-2\)
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)
once you have y = -x graphed, you shade above the boundary line why above? because of the > sign. This only works if y is isolated why is the boundary line solid? because there is an underline under the >
now do both graphs at the same time
the final step is to only shade where the two regions overlap one another
yeah pretty much
yeah you follow all those steps. Using desmos, or anything like it, is a good way to check the result