Question

Choose the system of inequalities that matches the graph below.
A.4x + y > 3
2x – 5y 15

B.4x + y 3
2x – 5y > 15

C.4x + y 3
2x – 5y < 15

D.4x + y > 3
2x – 5y 15

Answer 1

can you find the equations of the lines in the picture?

Answer 2

No

Answer 3

OK. lest work together!

Answer 4

first the solid line. OK?

Answer 5

the line passes through the points (0,-3) and (7.5,0)
is this right?

Answer 6

Yes

Answer 7

ok can you compute the slope?

Answer 8

Is it -2.5 ?

Answer 9

Or is it 0.4 ?

Answer 10

let's see
\[ \Large m_1=\frac{y_0-y_1}{x_0-x_1}=\frac{-3-0}{0-7.5}=\frac{-3}{-7.5}=0.4=\frac{2}{5} \]

Answer 11

did you do this?

Answer 12

Yes thats what I did !

Answer 13

remember (usually) it is always better to work with fractions that decimals!

Answer 14

Ok , but how will I make an equation out of this ?

Answer 15

good question!
we now have the slope and two points of the line!
the standard equation is
\[ \Large y-y_0=m_1(x-x_0) \]
can you find the equation?

Answer 16

you can use either one of the two points you have!

Answer 17

what would be the y and x ?

Answer 18

just keep the x and y. you have to replace x_0 and y_0.
for example you can use
\[ \Large (x_0,y_0)=(0,-3) \]
or
\[ \Large (x_0,y_0)=(7.5,0) \]

Answer 19

y+3=.4(x-0)

Answer 20

yes!
\[ \Large y+3=0.4x \]

Answer 21

can you do the same job for the dashed line?
the line passes through (0,3) and (0.75,0) (i'm not sure about this one) , right?

Answer 22

y-7.5=.4(x-0)

Answer 23

you got the same slope!
but this line goes from left to right. do you think this is right?

Answer 24

anyway. let' check
\[ \Large m_2=\frac{3-0}{0-0.75}=\frac{3}{-0.75}=-4 \]

Answer 25

y-7.5=-4(x-0)

Answer 26

almost
\[ \Large y-0.75=-4x \]

Answer 27

Ok so how do you make the equation ?

Answer 28

these are the equations!
but, do they look the same as in your problem?

Answer 29

No they don't relate to the answer choices.

Answer 30

so we turn our equations into the form you were given!

Answer 31

we first had:
\[ \Large y+3=0.4x=\frac{2}{5}x \]
so multiply by 5 and get
\[ \Large 5y+15=2x \]
rearranging
\[ \Large 2x-5y=15 \]
right?

Answer 32

do the same with the second!
\[ \Large y-0.75=-4x \]
remember
\[ \Large 0.75=\frac{3}{4} \]

Answer 33

Will the answer be a

Answer 34

i dont know!

Answer 35

you have some symbols missing
\[ 2x-5y\ ?\ 15 \]

Answer 36

let's try something easier!
i hope you got something of everything we did!

Answer 37

choose a point in the green region of your picture (the green region is where the yellow and blue regions meet).

Answer 38

Ok and yes I did thanks for helping me a little .

Answer 39

choose a point, say
\[ \Large (x,y)=(5,-5) \]

Answer 40

OK?

Answer 41

listen, i have to go 4 a while!
replace the point you chose into the sets of equations you have and you'll get the answer!