Question

The table below represents a linear function f(x) and the equation represents a function g(x).


x
f(x)
−1
−11
0
−1
1
9
g(x)

g(x) = 5x + 1



Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

Answer 1

x f(x)
-1, -11
0, -1
1, 9

Answer 2

that is a better graph of the numbers, i will award medals!!!

Answer 3

I can help you

Answer 4

yay!!
thanks!

Answer 5

So the first thing that you want to do is find the f(x) equation

Answer 6

ok i am having a little trouble with that

Answer 7

Since you know the x and y coordinates (f(x) basically means y), just plug 2 coordinates into the slope formula and you will get the slope for the f(x) equation

Answer 8

so i pick one of the coordinates ?

Answer 9

how about -1, -11

Answer 10

Pick two and plug them into the slope formula

Answer 11

The slope formula is \[y _{2}-y _{1}\div x _{2}-x\]

Answer 12

(-1,-11) would work now just pick another coordinate

Answer 13

and plug it in the formula

Answer 14

so -1 + 0 / -11 + -1?

Answer 15

give me a second to check that

Answer 16

Yes, that would work, now just solve it

Answer 17

ok so -1 divided by -12?

Answer 18

Yes so express that as a fraction to make it easier

Answer 19

-1/-12

Answer 20

the decimal is like .08333333333

Answer 21

so a fraction would be..

Answer 22

Ya, but you don't need to know the decimal

Answer 23

1/12?

Answer 24

yes!

Answer 25

awesome now what

Answer 26

Ok, so far the equation is f(x)=-1/-12x + b. b is the y intercept, to find it plug in one of the coordinates in for f(x) and (x).

Answer 27

so f(x)=-1/-12 + 9?

Answer 28

since its a y coordinate?

Answer 29

You almost got it, just put an x in after -1/-12

Answer 30

Now that you have that information you can solve both of the parts of the problem, since you know both of the slopes and the y-intercepts

Answer 31

oh whoops f(x)=-1/-12(0)=9

Answer 32

i mean1

Answer 33

i accidentally typed 0

Answer 34

Ok thats fine

Answer 35

so i solve it now?

Answer 36

so the y coordinate is negative 1 twelfth = 9?

Answer 37

I think your a little confused so lets take a step back. you have the equation f(x)=-1/-12x + b. Now plug in any coordinate for F(x) and x. Lets use the coordinate (1,9)

Answer 38

Plug in 9 for f(x) and 1 for x

Answer 39

ok so f(x)=-1/-12*1 = 9?

Answer 40

oooooh!!
ok

Answer 41

Yes!

Answer 42

9=-1/-12*1?

Answer 43

plus at the end whoops i switched it to =

Answer 44

9=-1/-12*1 + b, you can't forget the b because that is what your solving the equation for

Answer 45

ok

Answer 46

Sorry that took me a while, my computer froze

Answer 47

oh its fine

Answer 48

so now i have these :Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points

Answer 49

Ok so the slope for the f(x) equation is -1/-12 and the slope for the g(x) equation is 5, so the slope for g(x) is greater than the f(x) slope.

Answer 50

ok but how did u get 5?
i miss things sorry

Answer 51

From the g(x) equation that was given in the problem

Answer 52

ok

Answer 53

awesome i got part a now just: Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

Answer 54

would that be the g(x) one too?

Answer 55

And for part B, the y-intercept for the f(x) equation is 9 1/12 (let me know if you need help with finding the y-intercept) and for g(x) the y-intercept would be 1, so the f(x) function has the greater y-intercept

Answer 56

ok could you show me the steps u used?

Answer 57

F(x) would be greater bc 9 1/2>1

Answer 58

Ya I'll show you

Answer 59

Looks like I made a mistake...sorry the slope for f(x) is 1/12 bc -1/-12 simplifies to 1/12

Answer 60

oh ok

Answer 61

g(x) would still be greater though

Answer 62

So that means we should change the f(x) equation

Answer 63

so for A would the slope for the f(x) equation is 1/12 and the slope for the g(x) equation is 5, so the slope for g(x) is greater than the f(x) slope. work?

Answer 64

Yes

Answer 65

ok so now all i need is to justify how i got part b

Answer 66

I'm really sorry! But I need to go... if you need any more help I'm coming back at about 2:30 pm today

Answer 67

how'd u get it tho?

Answer 68

fx is still greater righT?

Answer 69

Yes

Answer 70

ok

Answer 71

The y-intercept is 8 1/12 for the f(x) equation, which is still much greater than f(x)

Answer 72

ok awesome thanks!

Answer 73

Your welcome...fan me I'm on twice a day every day and I'm always available to help (especially with algebra)