Question

determine the type of boundary line and shading for the graph of the inequality 5x+y>=-10
a.) dashed line with shading on the side that includes the origin
b.)solid line with shading on the side that does not include the origin
c.)dashed line with shading on the side that does not include the origin
d.)solid line with shading on the side that includes the origin

Answer 1

I know its either b or d

Answer 2

yes, ≥ means a solid line.

the origin means (0,0) which means x=0 and y=0
if you replace x and y with 0 in
5x+y ≥ -10
what do you get ?

Answer 3

5>=-10

Answer 4

5x*

Answer 5

no... try again.

remember 5x + y ≥ -10
means 5*x + y ≥ -10
erase the x, and put in 0. erase the y and put in 0
then simplify

Answer 6

it is b because it has the origin that be multiplied by x

Answer 7

@phi is it b?

Answer 8

if you replace x and y with 0 in
5x+y ≥ -10
what do you get ?

Answer 9

5(0)+0>=-10

Answer 10

yes. can you simplify the left side ?

Answer 11

5>=-10

Answer 12

5(0)+0>=-10

5 times 0 plus 0
remember order of operations. First do multiply, then add
so the first step is 5 times zero

Answer 13

so would it be 0??

Answer 14

yes, you get
0≥ -10

now, is that true ? Is 0 greater than or equal to -10 ?

Answer 15

If it were temperature, is 0 degrees bigger (warmer) than -10 degrees ?

Answer 16

yes

Answer 17

if 0≥ -10
that means (0,0) makes 5x+y≥ - 10 true.
you want to shade the side of the line that makes the equation true.

Answer 18

okay so the answer is b?

Answer 19

Here is what the line looks like.

Answer 20

one side of the line (meaning all the points on that side) make the relation true.
which side makes the relation
5x+y≥ - 10
true ?

Answer 21

left?

Answer 22

to answer the question, you pick a point (ANY POINT) on one side, and see if makes the relation true. If it does, then ALL the points on that side will make the relation true.

Answer 23

A really easy point to test is (0,0) (the arithmetic is easy)
if it "works" , that is the side you want to shade.

Answer 24

sooooooo out of the four answers d would be correct?

Answer 25

a.) dashed line with shading on the side that includes the origin
b.)solid line with shading on the side that does not include the origin
c.)dashed line with shading on the side that does not include the origin
d.)solid line with shading on the side that includes the origin

Answer 26

why ?

Answer 27

because it should be a solid line that has the origin

Answer 28

Here is how you would plot this problem

Answer 29

im confused is it b or d?

Answer 30

which side do you shade ?
the left side or the right side ?
which side is the origin on ?

Answer 31

you shade the side with the origin?

Answer 32

yes. which choice would that be?

Answer 33

d

Answer 34

notice if the problem were
5x+y ≤ - 10
the origin (0,0) would NOT WORK: 0 ≤ -10 is not true. You would shade the side that did not have the origin.

Answer 35

thanks :)