Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes?

f(x)= 3x − 3 (attatchment)

answer choices

The function f(x) has a larger slope.

The function g(x) has a larger slope.

They both have the same slope.

The relationship between slopes cannot be determined.

Answer 1

@texaschic101

Answer 2

do you know about slope-intercept form?

Answer 3

(y=mx+b) form?

Answer 4

yeah alittle

Answer 5

alright. do you know what the m and the b stand for?

Answer 6

m = slope ?

Answer 7

yes exactly

Answer 8

but what about B

Answer 9

b = the y-intercept (where the line crosses the y-axis)

Answer 10

ok so b = 2

Answer 11

yes good

Answer 12

now, do you know the slope= rise/run part?

Answer 13

no not at all

Answer 14

haha alright, ill explain. if you have a line (like you do) and you can find 2 different points on that line (ill help if you have some trouble with that) then you can count up or down and right or left units to find the rise over run part (again, i can help you)

Answer 15

i get the points part i just dont get the rise over run part

Answer 16

sorry im a little slow

Answer 17

thats fine ill help. so find your points on your line.

Answer 18

well.... notice those 2 points there

Answer 19

i highly recommend choosing your y-intercept and then another point on your line because it will be easier that way

Answer 20

sadly, yours doesnt give you an easy x-intercept or id recommend that as well, but for now just choose another point on your line

Answer 21

ok how about (1,5)

Answer 22

so notice the graph of g(x)

it really doesn't touch -1 at the bottom
so is not really 2, but is LESS than 2

Answer 23

perfect that will work ok so lets focus on the rise first. from 2 to 5 how much to you increase by?

Answer 24

now let's take a look at f(x) => \(\bf f(x)= {\color{brown}{ 3}}x -3 \\
\qquad \quad \uparrow \\
\qquad{\color{brown}{ slope}} \)

Answer 25

so slope is 3?

Answer 26

yes perfect because it goes up by 3 and over by 1 so your slope is 3/1 = 3

Answer 27

do you see how that works?

Answer 28

if youre confused i can try to explain in a different way

Answer 29

yeah im getting the rise over run part now

Answer 30

awesome. alright so then for these two lines your answer would be that the slopes are the same

Answer 31

oh wow it ended up being easy lol thanks so much. really do appreciate it