Question

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


x f(x)
−1 −9
0 −1
1 7
g(x)

g(x) = 3x − 2


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

`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)`

focus on the first two rows of the table

x y
-1 -9
0 -1

hopefully you agree that those two rows mean we have these two points (-1,-9) and (0,-1) ?

Answer 2

yea i do

Answer 3

what is the slope of the line through the two points (-1,-9) and (0,-1) ?

Answer 4

slope formula
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 5

ok hold on

Answer 6

-8/-1

Answer 7

which reduces to what?

Answer 8

idk

Answer 9

two negatives divide to make a positive, so 8/1 = 8

Answer 10

i think that is all it reduces to

Answer 11

(-8)/(-1) = 8/1 = 8

Answer 12

oh that make sense

Answer 13

so the slope of f(x) is 8

Answer 14

what is the slope of g(x) ?

Answer 15

how do u find that

Answer 16

are you familiar with y = mx+b?

Answer 17

yes

Answer 18

with y = mx+b, m is the slope

Answer 19

so compare y = 3x-2 with y = mx+b

do you notice how the '3' and the 'm' match up? do you see how they're in front of the x?

Answer 20

yea

Answer 21

so you would agree that the slope of g(x) is 3 ?

Answer 22

yes i agree

Answer 23

summary:
slope of f(x) is 8
slope of g(x) is 3

we can see that f(x) has a larger slope

Answer 24

yes

Answer 25

so that is part b right

Answer 26

also what would i write as a comparison in part a

Answer 27

@jim_thompson5910

Answer 28

@jim_thompson5910

Answer 29

are u there

Answer 30

sorry about that

Answer 31

that was all for part A

Answer 32

so we begin with part B

Answer 33

yes let's look at part B now

Answer 34

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

Look at the table. What is the y value when x = 0?

Answer 35

-1

Answer 36

so -1 is the y intercept for f(x)

Answer 37

what is the y intercept for g(x) ?

Answer 38

hint: y = mx+b
m = slope
b = y intercept

Answer 39

i am not sure

Answer 40

compare y = 3x-2 to y = mx+b

m = 3
b = -2

agreed?

Answer 41

agreed

Answer 42

b = -2 is the y intercept of g(x)

Answer 43

y intercept of f(x) is -1
y intercept of g(x) is -2

Answer 44

so we see that f(x) has the greater y intercept because -1 is larger than -2

Answer 45

so g(x) has the higher y intercept

Answer 46

-2 is below -1

Answer 47

draw out a vertical number line like so

Answer 48

oh right so -1 is higher i was thinkin that they were positive sorry