Question

Look at this function:


x y
−12 −8
−8 −6
−4 −4
0 −2


Mina said that the function is linear.

Jenna said that the function is nonlinear.

Which of the following explains who is correct?
Mina, because for every 2-unit increase in x, there is an increase in y by 4
Mina, because for every 4-unit increase in x, there is an increase in y by 2
Jenna, because the point (0, −2) does not lie on the straight line that contains the other points
Jenna, because the point (−12, −8) does not lie on the straight line that contains the other points

Answer 1

sorry its all smooshed together

Answer 2

well let's look at the reasons...
what number is x increasing by each time?
what number is y increasing by each time?

Answer 3

x=4

Answer 4

y=2

Answer 5

right because -12+4 gives us the next number -8 for x
and yes -8+2 gives us the next number -6 for y
so we definitely know it isn't option A because that explanation is kinda backwards

Answer 6

so B looks like a good candidate

we can also look at Jenna's reasonings

Answer 7

yeah ok cross out A

Answer 8

linear functions can be written as f(x)=mx+b

Answer 9

anything that can be written as f(x)+mx+b is a liner function
m and b can both be zero

Answer 10

hmm so C

Answer 11

oops f(x)=mx+b *
do you know how to attempt to find this line given two points
say (-4,-4) and (0,-2)

Answer 12

or is that crossed out

Answer 13

i son't sorry but i can try figureing it out:()

Answer 14

the slope represents m
\[m=\frac{y_1-y_2}{x_1-x_2} =\frac{-2-(-4)}{0-(-4)}\]

Answer 15

what is -2+4 and 0+4?

Answer 16

2 and 4

Answer 17

right!
\[f(x)=\frac{2}{4}x+b \\ \text{ we can reduce the slope number there } \\ f(x)=\frac{1}{2}x+b \\ \text{ now using either point we can come up with b } \\ f(-4)=\frac{1}{2}(-4)+b=-4 \\ \\ \text{ so we need \to solve } \\ \frac{1}{2}(-4)+b=-4 \\ -2+b=4\]
do you know what b is?

Answer 18

some glitching is happening sorry

Answer 19

didnt mean to say that... i get it

Answer 20

B= 6?

Answer 21

well I left the - off on my 4 in the next line
the last should have been -2+b=-4

Answer 22

so b=-2

Answer 23

oh ok thanks

Answer 24

\[f(x)=\frac{1}{2}x-2 \\ \]
let's look at your points and see this linear equation works for all of them:
\[f(-12)=\frac{1}{2}(-12)-2=-6-2=-8 \text{ \check mark for the first point } \\ f(-8)=\frac{1}{2}(-8)-2=-4-2=-6 \text{ \check for mark the second point } \\ f(-4)=\frac{1}{2}(-4)-2=-2-2=-4 \text{ \check mark for the third point }\]
and you check the last one if you want to

anyways what this says is jenna is totally wrong since we were able to describe the points in the chart with a linear function

Answer 25

so if you can spot a similar pattern like mina did you can determine it is linear from that

Answer 26

so neither is mina and not A either so its B?

Answer 27

yep it is B
it is the correct answer with a correct reasoning

Answer 28

thx now i know what i am doing you have helped a lot thank you so much:)

Answer 29

np