Question

medal and fan!

Answer 1

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

Answer 2

X F(X) G(X)
-1 -11 Gx=5x+1
0 -1
1 9

Answer 3

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 4

that is it

Answer 5

@dan815

Answer 6

@ganeshie8

Answer 7

@Keigh2015

Answer 8

@Michele_Laino

Answer 9

@tkhunny

Answer 10

hint:
the slope of a linear function like this one:
\(F(x)=ax+b\), is given by the coefficient \(a\)
So, what is the slope of the function \(G(x)\) ?

Answer 11

i dont know how to do that

Answer 12

we have this \(G(x)=5 x +1\)
what is the coefficient which multiplies the variable \(x\) ?

Answer 13

5?

Answer 14

correct! So the slope of the function \(G(x)\) is \(5\)

Answer 15

okay now what!?!

Answer 16

now, we have to write the equation of the function \(F(x)\) using the data you provided

Answer 17

F(5)?

Answer 18

in order to do that, we can use this general formula:
\(F(x)=ax+b\), and, by means of the data above, we have to establish the values of the coefficients \(a\) and \(b\)

Answer 19

now, I consider the second point \((0,-1)\)
namely when \(x=0\), \(F(x)=-1\), so I replace those value in my general formula:
\[ \Large - 1 = a \cdot 0 + b\]
please what is \(b\) ?

Answer 20

values*

Answer 21

b=-1

Answer 22

correct! :)
so I update my formula above, and I get:
\(F(x)=ax-1\)

Answer 23

nxt I consider the third point \((1,9)\), and, as before, I replace \(x=1\) and \(F(x)=9\) into my equation, so I get:
\(9=a \cdot 1-1\)
please what is \(a\) ?

Answer 24

a=10

Answer 25

that's right! :)
so the formula of \(F(x)\), is:
\(F(x)=10x-1\)
Now, I ask what is the coefficient which multiplies the variable \(x\) ?

Answer 26

10?

Answer 27

that's right! We can say that the slope of \(F(x)\) is \(10\)

Answer 28

okay so how would i write all this in a way that it answers the question?

Answer 29

we can answer to part A, saying that the slope of \(F(x)\) is \(10\), whereas the slope of \(G(x)\) is \(5\)

Answer 30

of course, please you have to write all my steps

Answer 31

okay and can we do part b please?

Answer 32

for part B, we have to keep in mind that when we have the subsequent equation:
\(f(x)=ax+b\)
the \(y-\)intercept is the coefficient \(b\)

Answer 33

so, what is the y-intercept of the function \(F(x)\) ?

Answer 34

not sure how to do that

Answer 35

we have:
\(F(x)=5x+1\)
if I replace \(x=0\), then I can write:
\(F(0)=5 \cdot 0+1=...?\)

Answer 36

please continue

Answer 37

1?

Answer 38

correct! So we can say that the y-intercept of \(F(x)\) is \(1\)

Answer 39

similarly, if I replace \(x=0\) into the equation for \(G(x)\), I get:
\(G(0)=10 \cdot 0-1=...\)
please continue

Answer 40

-1

Answer 41

that's right!! So, we can say that the y-intercept of \(G(x)\) is \(-1\)

Answer 42

is that it for part b?

Answer 43

yes! Since we can say that the y-intercept of F(x) is greater than the y-intercept of G(x)

Answer 44

okay i will give you a medal but can you stay here so that i can show you what i am going to put on my assignment?

Answer 45

ok!

Answer 46

thank you!

Answer 47

:)

Answer 48

part a:
F(x)=ax+b
g(x)=5x+1
g(x)=5

f(x)=ax+b
-1=a * 0+b
b=-1

f(x) = ax -1
9=a * 1-1
a=10
f(x) =10x-1

slope of f(x) =10
slope of g(x)=5


Part B:
f(x)=ax+b
F(x) = 5x+1
F(0)=5 * 0+1
F(x)=1

G(x)=10x-1
G(0)=10 * 0-1
G(x)=-1

Answer 49

@Michele_Laino im done

Answer 50

is this right @Michele_Laino

Answer 51

anything you could add?

Answer 52

yes! Please you have to add this statement:
"From my computation above, I conclude that the y-intercept of F(x), is greater than the y-intercept of G(x)"

Answer 53

where would i write that for part a or b?

Answer 54

for part B

Answer 55

thank you so much @Michele_Laino

Answer 56

:)