Question

Which of the following systems of inequalities would produce the region indicated on the graph?
(will post graph and answer choices in a sec!!!)

***PLease explain!! :) Thank youuuu :)

Answer 1

GRAPH

Answer 2

Answer choices A,B,C,D (top to bottom)

Answer 3

we have 2 lines here

Answer 4

we can find the equations of these lines by locating the points on the lines

Answer 5

mhmm and one is solid and one is dotted... do we need to know that part??

Answer 6

so for instance, the line sloping downward has the points (0,4) and (4,0)

Answer 7

yes that's important info as well

Answer 8

yup i see that :)

Answer 9

what is the equation of the line that goes through (0,4) and (4,0)

Answer 10

it goes thru (0,2) ??

Answer 11

that's a different line

Answer 12

ohhh okay nvm hahaa hold on lemme see

Answer 13

slope is -1 right?

Answer 14

yes, slope is -1

Answer 15

for the solid line

Answer 16

yup :) and is the y intercept 4?? the y-int is off the vertical axis (y axis) right??

Answer 17

exactly

Answer 18

so the equation is y = ??x + ??

Answer 19

so the equation for the solid line is y=-x+4

(i don't need to write -1x right? -x is fine?)

Answer 20

-x is just fine

Answer 21

ys, y = -x+4 is the equation of the boundary line

Answer 22

yes*

Answer 23

so because the shading is below this solid boundary line, you use the \(\Large \le\) symbol

Answer 24

to get \(\Large y \le -x+4\)

Answer 25

haha typos... we hate them! lol :) oh okay i see :) that makes sense :) what next?

Answer 26

ys i hate typos lol (totally intentional...hmm probably killed the joke though)

Answer 27

use the same idea to find the inequality for the second piece

Answer 28

lawlz i see what you did there! hahaa :) good one :) and so we are at the second line now?? the dotted one?

Answer 29

yes, what is the equation of that boundary line?

Answer 30

the dotted one?

Answer 31

yes

Answer 32

any ideas?

Answer 33

ummm so the point is (0,2) right?? so the y-intercept is 2 yes?

Answer 34

good so far, what's another point?

or what's the slope?

Answer 35

and the slope looks like it is 1 right? is the slop=1?

Answer 36

good

Answer 37

so the equation is y = x+2

Answer 38

another point would be (1,3)

Answer 39

right?

Answer 40

yes, another point is (1,3)

Answer 41

the line is dashed and we're shading below it, so the inequality is

y < x+2

Answer 42

hmm something seems weird...it's like some of your messages aren't getting through?

Answer 43

so is this the answer?? answer A?? \[y \le -x +4;y <x +2;y \ge0,x \ge0\]

Answer 44

is that right?? answer A?

Answer 45

exactly, A is the answer

Answer 46

and yeah it's weird right?? i had to retype that :( oooh!! yay :) thanks!!! :)

Answer 47

lame, i hate when that happens