!!!!!!

Algebra!I!Notes:!Graphing!Linear!Functions!Slope!Intercept!Form!

!!!!!!!!!!

Example!1:!Determine!if!point! 2,4 !is!on!the!line!! ! = !! ! − 1?!

!Method!1:!Graphically!!

Method!2:!Algebraically!graphtheline doeslhepointmaketheequationtrue ?Lslookmdseetisthepointontheline ?

411*-1not ,÷xhe 7

k4÷3-1

A ,4 ) •

• 412{ri No3og

the point Dnstontheline

*'s

!Recall:!The!parent!linear!function!is!! ! = !!!Example!2:!Graph!the!function!and!then!compare!the!graph!to!the!parent!linear!function.!! ! = ! + 3!!!!!!!!!!!!!

& XP

gkdhasadiffoerty .int.

•c- parent function

B. •

fk )

• •

gkdisshifledup •

3 units •

!Direct!Variation—a!function!in!the!form!! ! = !"!or!! = !"!where!! ≠ 0!!!!—constant!of!variation!!!formula!for!the!constant!of!variation:!!!!!!!!!

theseare

c- Slope JustProblems

W1%intof o

y¥T x

sbpe→K=¥

.

Example!3:!Find!the!constant!of!variation!! ! = !

! !!Try!it:!Find!the!constant!of!variation!! = −!!

!!!!

2- - 1

3

Example!4:!Determine!if!the!equation!is!an!example!of!direct!variation.!If!it!is,!find!the!constant!of!variation.!! = 2! + 1!!

Try!it:!Determine!if!the!equation!is!an!example!of!direct!variation.!If!it!is,!find!the!constant!of!variation.!

! = −3!!

Try!it:!Determine!if!the!equation!is!an!example!of!direct!variation.!If!it!is,!find!the!constant!of!variation.!

−! = 10!!!

Try!it:!Determine!if!the!equation!is!an!example!of!direct!variation.!If!it!is,!find!the!constant!of!variation.!!!

!

No, yint is not 0 Yes

. y- int is 0

k =-3

To to fftmiitbb Yesy=ff if b :O its K .

- ID. V

.

÷o=K

Example!5:!Write!an!equation!for!a!direct!variation!that!includes!the!point!(−8,10)!

Example!6:!Assume!that!!!varies!directly!with!!.!If!! = 28!when!! = 7,!find!!!when!! = 52.!

!

itK=¥ × y

K=¥=0¥=4K=Hg=§

y=4xwhat is xwhuy -52 ?

.

52=4×-44y=Kx ytfx

is :X