Question

determine the type of boundary line and shading for the graph of the inequality -4x-y<-2

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

hi.

Answer 2

can you help me?? :/

Answer 3

i can.

Answer 4

im like completely lost!

Answer 5

ok. it is allright. now, can you get the y on the other side of the inequality sign?

Answer 6

try adding y to both sides of the inequality.

Answer 7

no D:

Answer 8

okay

Answer 9

now, add the two to both sides

Answer 10

okay!

Answer 11

remember the only thing different about operating on a linear inequality and a linear equation is that if you multiply or divide the inequality by a negative number, you have to switch the inequality direction

Answer 12

so it switches ?

Answer 13

you should have something like this: y>-4x+2

Answer 14

yes

Answer 15

the inequality switches ONLY if you multiply or divide by a NEGATIVE number. we have not actually done that here, but i mention it because if you can solve linear equations, then you can solve inequalities as long as you remember the rule about neg numbers

Answer 16

oh okay...

Answer 17

good to know

Answer 18

ok. now, the line determined by y=-4x+2 is the boundary

Answer 19

ok

Answer 20

but do we use a dashed or solid line? hmmmmm....

Answer 21

dashed?

Answer 22

well, solid lines are used when the inequality contains an = sign. so yes, dashed is correct. fantastic. nicely done

Answer 23

yay!

Answer 24

now, the part you color in contains all the points where the y coordinate is greater than or 'above' the dashed line.

Answer 25

so the graph kinda cuts the paper into two pieces. One part you color and one part you dont

Answer 26

can you graph the line?

Answer 27

it will go downward from left to right because it has a negative slope and a y intercept of +2

Answer 28

did you graph the line?

Answer 29

yes

Answer 30

ok, now the area you want to color because of the y> part is above the graph

Answer 31

ok

Answer 32

so it is going to be on the top right side of the paper

Answer 33

right

Answer 34

ok, i think you are done. any other questions?

Answer 35

but is it with or without the origin
?

Answer 36

without the origin

Answer 37

ohhh ok! thanks

Answer 38

graphit and it will make sense'

Answer 39

take care