E) SLOPE:

The

slope

formula:

Given 2

points

(u,b)

&

(c,d),

the slope

ofthe line

connecting

these

points

is given

by

the

formula:

m

:

(d-b)/(c-a)

:

(b-d)(a-c)

or

m

:AylAx

i.e., (change

in

y

over

change io *), (rise/run)

Example:

Find

the

slope

of the line

connecting

the 2

points

(1,-%)

and

(-2.1/5).

Solution:

m

:

[1/s-(-%))/(-2-1)

:

(1/5+%y(-3)

:

(z+sy(-30)

:

7I(-30): -7

t30

F)

EQUATIONS

OF

LINES:

1)

FORM

#1)

(Slope-intercept

form): y

:

mx

*

b,

slope is

the

coefficient

of x.

2)

FORM

#2)

(point-slope

form):

y-d:

m(x-a)

where

(a,d)

is

any

point

on the

line.

Note:

This is

the most

popular

form

used

in calculus.

3)

FORM

#3)

(general

form):

Ax+By+C:0

Note:

There

are certain

problems

where

general

form is

necessary.

Note:

There

are more

forms

of

an

equation

of

a line

that

are not

grven

here.

Note:

To

find

the

slope

given

the

equation,

use form

#1.

Note:

To

write

the

equation

quickly

given

a

point

& slope,

use

form

#2.

Note:

To

make

a

quick

sketch

of

the line,

use form

#1,

b is

the

y-intercept

for

the line.

Exarrrple:

Write

an equation

ofthe line

containing

the

points

(\,-yr)

&,

(-z,Il5).

Solution:

m:

-7130

(see

previous

example).

Choose

either

point

and

use

point-slope

form:

We

get, y+%:

(-7130)(x-1)

Example:

Find

the

slope

ofthe

line

33x-7y-22:0.

Solve for y

and

use

form

#l

to look

form.

Solution:

33x-7y-22:0

->

33x-22:Ty

+ 33x17 -2217

:y

-+

(3317)x

-2217:

y

+

m: 3317