Question

HElp me please!!!!!!!!

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

now use x = 1

if x = 1, then y = ???

Answer 5

you did it right

Answer 6

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

Answer 7

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

Answer 8

yeah because of that underline

Answer 9

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

Answer 10

we can use desmos to graph

https://www.desmos.com/calculator

Answer 11

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

Answer 12

good

Answer 13

as for the other inequality

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

Answer 14

you'll need to graph y = -x

then shade above that solid boundary line

Answer 15

notice how in your desmos graph, the shading is above the boundary line

because of the > symbol

Answer 16

do you know how to graph y = -x ?

Answer 17

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

Answer 18

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

Answer 19

so one point on it is (0,0)

Answer 20

then if x = 1, y = ???

Answer 21

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

Answer 22

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 >

Answer 23

now do both graphs at the same time

Answer 24

very good

Answer 25

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

Answer 26

yeah pretty much

Answer 27

yeah you follow all those steps. Using desmos, or anything like it, is a good way to check the result

Answer 28

no problem