Question

Which of the following inequalities matches the graph?

Answer 1

-6x + y < 3

6x + y < 3

6x - y < -3

The correct inequality is not listed

Answer 2

@helder_edwin

Answer 3

can u see that the point (-4,2) is in the shaded area?

Answer 4

yes

Answer 5

(this point is arbitrary, u could have chosen any point in the shaded area)

then u have x=-4 and y=2.
now replace these in every inequality u r given

Answer 6

for instance
\[ \large -6x+y<3 \]
\[ \large -6(-4)+2<3 \]
\[ \large 24+2<3 \]
\[ \large 26<3 \]
is this true?

Answer 7

it is not.

Answer 8

then pass to the second

Answer 9

\[ \large 6x+y<3 \]
\[ \large 6(-4)+2<3 \]
\[ \large -24+2<3 \]
\[ \large -22<3 \]
is this true?

Answer 10

true

Answer 11

how about the third one?
\[ \large 6x-y<-3 \]
\[ \large 6(-4)-2<-3 \]
\[ \large -24-2<-3 \]
\[ \large -26<-3 \]
is this true?

Answer 12

also true

Answer 13

then u have two possible answers
\[ \large 6x-y<-3 \]
or
\[ \large 6x+y<3 \]

Answer 14

but which one matches the graph?

Answer 15

do u see the line that limits the shaded area?

Answer 16

yes

Answer 17

does it have positive or negative slope?

Answer 18

from left to right??

Answer 19

positive slope

Answer 20

yes :)

Answer 21

if we write = instead of < then
\[ \large 6x+y=3\Rightarrow y=-6x+3 \]
negative slope

Answer 22

but
\[ \large 6x-y=-3\Rightarrow y=6x+3 \]
positive slope

Answer 23

then the answer is
\[ \large 6x-y<-3 \]

Answer 24

ohhh so its C :)

Answer 25

Thank you !! (;

Answer 26

u r very welcome