Question

Two linear functions are represented in different formats.

Function 1:
x y
−2 ​ −1 ​
0 ​1
2 ​3
5 ​6
Function 2:

Graph: (-1,-4) (2,7)

Which statements are true?

Select each correct answer.


Function 1 has a greater rate of change than function 2.

Function 2 has a greater rate of change than function 1.

Function 1 has a greater y-intercept than function 2.

Function 2 has a greater y-intercept than function 1.

Answer 1

Function 1 has the two points (-2,-1) and (0,1)

Do you know how to find the slope of the line through these two points?

Answer 2

no

Answer 3

do you need help?

Answer 4

yes please!

Answer 5

ok

Answer 6

First you subtract the y coordinates:
-1-1 = -2
Then subtract the x coordinates in the same order
-2-0 = -2
Lastly you divide the two results
(-2)/(-2) = 1
So the slope of the first function is 1

Answer 7

Hopefully that makes sense. If so, then please tell me what the slope of function 2 would be.

Answer 8

so would it be m=-11/-3 ?

Answer 9

that can be simplified further

Answer 10

so then it would be 3 1/3 ?

Answer 11

Yes

Answer 12

11/3 is not the same as 3 & 1/3

Answer 13

ya thats what i meant

Answer 14

wait now im confused

Answer 15

11/3 is correct though
As a decimal, it would be roughly 11/3 = 3.67

Answer 16

Function 1 has a slope of 1
Function 2 has a slope of 11/3 = 3.67
Now you select which is larger

You'll also need to check the y intercepts of each function as well.

Answer 17

function 2 is larger

Answer 18

yes function 2 has the larger slope

Now you'll have to compare the y intercepts

Answer 19

and how do i do that

Answer 20

In the table, look where x = 0. What is the paired y value for this x value?

Answer 21

1

Answer 22

yes, so the y intercept is 1 here

For function 2, it's not as quick, but it's not too bad

We found the slope to be m = 11/3
We'll use this along with the point (x,y) = (-1,-4) to find the y intercept value b

Recall that y = mx+b has m as the slope and b as the y intercept

So,
y = mx+b
-4 = (11/3)*(-1) + b
-4 = -11/3 + b
3*(-4) = 3(-11/3 + b)
-12 = -11 + 3b
I'll let you finish up and solve for b. I multiplied both sides by 3 to clear out the fraction.

Answer 23

so if im doing this right 26=b

Answer 24

incorrect

Answer 25

sorry -26=b

Answer 26

think of
-12 = -11 + 3b
as
-12 = 3b-11
which is the same as
3b-11 = -12

Answer 27

how would you solve 3b-11 = -12 ?

Answer 28

would it be 15?

Answer 29

first we add 11 to both sides, agreed?

Answer 30

ya

Answer 31

that would make it =-1 right?

Answer 32

That means 3b-11 = -12 becomes 3b-11+11 = -12+11

The -11+11 turns into 0
the -12+11 turns into -1

Answer 33

yes you beat me to it

Answer 34

so we now have 3b = -1

Answer 35

Now we need to fully isolate b

Answer 36

then you divide?

Answer 37

yes

Answer 38

so would it be -1/3

Answer 39

yep b = -1/3
that's the y intercept of function 2

Answer 40

summary:
y intercept of function 1 is 1
y intercept of function 2 is -1/3

Answer 41

so function 1 is greater

Answer 42

yes

Answer 43

omg thanks

Answer 44

you helped me a lot

Answer 45

I'm glad I could help