Question

Help with linear functions
(Image Included)

Answer 1

Please take a better photo. I cannot read the entirety of the question or the answers.

Answer 2

okay. @TheDebunker

Answer 3

Is this is a better image ? @TheDebunker

Answer 4

Scoot back a little.

Answer 5

The questions asks:
Which relationship does NOT represent a linear function?

The answer choices are:
A. the total cost of a large pizza based on $9.95 plus 0.75 for each additional topping
B. The ant population for a colony that begins with 5 ants and doubles in number every two weeks
C. the amount of gasoline in a vehicle that begins with 22 gallons and decreases by one gallon every 28 miles
D. a history students's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly

Answer 6

@TheDebunker

Answer 7

@bellezabrilla do you know what mean ,,linear function" ?

Answer 8

a linear function creates a line

Answer 9

Yeah..

Answer 10

ok. so than you check this choices what you think that not will result a line like a graph ?

Answer 11

the first one is clearly sure - yes ?

Answer 12

@danie007 your opinion about ?

Answer 13

@bellezabrilla the second is clearly ?

Answer 14

no

Answer 15

NO B

Answer 16

why not D and why B ?

Answer 17

in case of B the population is doubled in 5 weeks - so this is a line sure

Answer 18

sorry in every two weeks and not 5 sorry

Answer 19

Alright. Linear functions are always constant. Example

X: 1 2 3 4 5
-----------------
Y: 2 4 6 8 10

This is a linear function because as the X axis increases by one, the Y axis increases by 2. It is always consistent.

Non linear functions are the opposites of linear functions. Example

X: 1 2 3 4 5
----------------
Y: 2 5 9 14 22

This is a non linear function because it is not constant. Even though the X axis increases by 1, the Y axis doesn't have any kind of consistency, which makes it look weird on a graph.

Using this information, what do you think the answer is?

Answer 20

yes this is right but in case of C. these cantitie of gasoline decreasing constant

Answer 21

but in case of D. how you see it ?

Answer 22

@TheDebunker uh --- I think it's B due to the fact that in week 1 there's 5 ants..... then in week 2 there's 10

Answer 23

Every week the population of the ants increases by 5. that means it's consistent. Remember, for it NOT to be a linear function, it has to be inconsistent.

Answer 24

Oh yeah I totally forgot what the question asked for

Answer 25

Okay so it's not B @TheDebunker

Answer 26

@jhonyy9 I'm confused

Answer 27

why ? the @TheDebunker explication is very very right and good

Answer 28

Alright how about this?

Graph these answers on a graph and tell me which one does not make a straight line. The one that looks like it's bending upwards or downwards is they answer you want. It has to be a straight line to be linear.

Answer 29

The answer you want is B. Why?

Every 2 weeks, the population doubles. There are 5 to start out with.

X: 2 4 6 8 10
-----------------------
Y: 5 10 20 40 80

As you see, the Y axis is not consistent like the X axis. Hopefully we helped you understand this problem a little bit better.