Question

suppose f(x) = ax+b where a and be are constants. if f(1)=7 and f(3)=5, find a and b.

Answer 1

Ok, \(f(1)=7\) means that

\(\color{#000000 }{ \displaystyle f(1) = a\cdot (1)+b=7 }\)
\(\color{#000000 }{ \displaystyle a+b=7 }\)

Answer 2

ok...i kinda get it

Answer 3

plug in f(3)=5 into the function (as I did with f(1)=7)
and you will have the second equation

Answer 4

ok so then it becomes \[f(3)=a(3)+b=-5\]

Answer 5

am i correct or..?

Answer 6

-5 ?

Answer 7

sorry, the f(3)=-5

Answer 8

i made a typo up above

Answer 9

I thought the 5 was positive

Answer 10

oh, typo, ok

Answer 11

yea haha sorry. so do we leave the equations like so or do we do more with them

Answer 12

yes, and a(3), is same thing as a•3, so you can just write
\(\color{#000000 }{ \displaystyle 3a+b=-5 }\)

Answer 13

So you were given
f(1)=7 and f(3)=-5

and thanks to that we have the two equations below,
\(\color{#000000 }{ \displaystyle a+b=7 }\)
\(\color{#000000 }{ \displaystyle 3a+b=-5 }\)

which is just a system of equations.

Answer 14

the back of my book says the answers are a=-6 and b=13

Answer 15

and you want to know why...

Answer 16

*(duh)*

Answer 17

yes please lol

Answer 18

first, is it clear how we obtained the system of equations below?

\(\color{#000000 }{ \displaystyle a+b=7 }\)
\(\color{#000000 }{ \displaystyle 3a+b=-5 }\)

Answer 19

yes

Answer 20

You can subtract b on both sides of the first equation, and what wll this give you?

Answer 21

um you get \[a=7-b\]

Answer 22

i think

Answer 23

yes, and substitute this into the second equation for a

\(\color{#000000 }{ \displaystyle 3(7-b)+b=-5 }\)

Answer 24

then expand and simplify the left side

Answer 25

ok so then you get \[21-2b=-5\]

Answer 26

then subtract 21 from 5, you get -16/2b

Answer 27

which is -8

Answer 28

is that correct?

Answer 29

for b?

Answer 30

wait no i got it wrong

Answer 31

oh wait haha i see what i did wrong, ok b=13

Answer 32

now that i know that, how do i get a?

Answer 33

oh wait you would just subtract 7-13=-6

Answer 34

ok hahaha makes so much sense now

Answer 35

21−2b=−5
−2b=−5-21

Answer 36

-26

Answer 37

not -16

Answer 38

yea haha i see what i did wrong

Answer 39

and b is?

Answer 40

13

Answer 41

as given in answers...

Answer 42

b is 13 in the back of the book...

Answer 43

yes

Answer 44

and then the a,

a+b=7
a+13=7
a=...

Answer 45

great! ok if u dont mind me asking, how long will you be online for? a is -6

Answer 46

i just wanna know just in case i accidentally bother you lol

Answer 47

No, it is fine... we all make simple error. But when teachers take off 10 points off for that, they are pigs !

Answer 48

yw, and good luck

Answer 49

haha thanks