ClassMeeting

#2

Linear

Fungtioqq

-The

graph

of a

linear

function

is

a

straight

line

or segment

-These

graphs

have

the

same slope

at

all

points

Slopesr

horizontal

(zero),

vertical

(not

defined),

slants

right

(+),

slants

Ieft

G)

Ay

means

*the

change

in

y''

=

y2

*

yr

Ax

means'the change

inx'=

x2

-

xl

Slope

is

defined as

rn

=

AylAr

:

(Jz-

yr/(xz

-

xr)

This number

rspresents the slope of a

line

passing

Though

or

containing the

points

Pr &

Pz

Writlne

en eouation of

a

linear function

-There

are many

forms

for

linear

equationg

however, in

basic

courses, the

following 2 are

used

most

of

the time.

Slppe.:intergept

form:

y

=

ilrx

+

b

(m

is

the

slope & b is the

y-intercept)

Examples:

a)

y

=3x

+2

defines a

line with

slope

3

&

y-intercery/.z

b)

y

=

G2l5)x

-

7

defines a

line

with

slope

-2l5

&

y-intercept

-7

Point:slopg

for.m:

y

-

yl

=

m(x

-

xr),

where

(xr,yr)

is

any

point

on

ttre

line

Examples:

a)

y

-

3=

4(x- 2)

defines

a

line

containrng

the

point (43)

with slopg =

4

b)

yr7=

-3(x+J) defines a line

containing

the

point (-5,-7)

with slope

=

-3

Example

Write the

equation of iline

wittr

slope

5

and

crosses

tle

y-a,xis

at

-3...Do.

Exanrple; \Yrite

the equation of a

line

passing

through

tlre two

points (3,5)

&

(2,7)...Do

-Any

equation

in

poiut-slope

form may be written

in

slope-intercept

form

by simply

clearing

pareiltheses

&

solving

for

y.

-When

going

from

slope-intercept

to

point-slope

forfi! use

the

point (0,b)

for

the

point.

^General

form

is

also

popular

but

does

not

give

much information: Ax

+By +C=0