Standard Form And Point Slope Form

First, Some Important slides from last time! Take Some Notes!

Review: Slope-Intercept Form

y mx b Slope Y-int.

riseslope mrun

= Change in y =

= Change in x =

yx

Slope describes a lines its steepness, incline, decline or grade.

calculate Slope With 2 Points

we have a point (x1, y1) and another point (x2, y2)

(x1, y1)

(x2, y2)

Change in y (rise) over the Change in x (run).

It looks likes this.

2 1

2 1

( )( )y yx x

Review: Calculating Slope

yx

=

Review: Finding x-int, and y-int

• Remember, to find x-int, plug in 0 for y and Solve.

• To find y-int, plug in 0 for x.

• Horizontal Lines Have no x intercept, 0 slope and equal the y-intercept!

• Vertical Lines have no y intercept, an undefined slope and equal the x intercept!

Other forms of A Line

• Just Like there are other forms of to represent fractions, there are different ways to represent a line.

• Example:

• What are some other instances when you see things in other forms?

1 31 1.52 2

Standard Form

• Another way to write the equation of a line is using Standard Form.

• A,B and C are real numbers and A and B can not be zero.

Ax By C

Slope-Int Form to Standard Form

• Suppose we wanted to see the equation of a line in standard form from slope-int form.

• Here is what we do: • Example #1

3 4y x 3 3x x

3 4x y Seriously? That’s it! Dude! Piece of Cake!

A = -3B = 1C = 4

Slope-Int Form to Standard Form

• Example #21 156

y x 1 16 6x x

1 156x y

Seriously? That’s it! Hot Dog! Piece of Cake!

A = -1/6B = 1C = -15

Standard Form to Slope-Int Form

• Example #3 8x + 4y = 16

-8x -8x

4y = -8x + 16 Are we finished???NO!

/4 /4 /4

y = -2x + 4

Cereal? That’s it! Hot Dog! Easy as Pie!

Standard form (x- and y-int)

• How to find x and y int? Just plug in zero for x or y!

• Example #48x + 4y = 16

8(0) + 4y = 164y = 16

/4 /4

y = 4

8x + 4(0) = 168x = 16/8 /8

x = 2

Find y-int, plug in zero for x! Find x-int, plug in zero for y!

Wowsers!

Point-Slope Form

• The last form we will look at is Point-Slope Form. The hole point (Get it) of this form is an easy way to write an equation for a line using the slope, and a point (Hence the name!).

• The Form is….. • Drum Roll Tap those fingers on your desk!

1 1( )y y m x x

Point-Slope Form• Let us see how we make an equation using

Point-Slope Form.• Given that Slope equals 3 and a point (2,4),

write an equation of a line using point-slope form.

• What do we do?• We have m and x1,y1.. so..• Plug and Chug!

1 1( )y y m x x

1 13( )y y x x 1 1( )y y m x x

4 3( 2)y x

An you leave it!

One mo Time…• Slope equals -6 and a point (-2,-4), write an

equation of a line using point-slope form.• Plug and Chug!

1 16( )y y x x 1 1( )y y m x x

( 4) 6( ( 2))y x

No Way, Really? That is Simple!

4 6( 2)y x

1 1( )y y m x x

Point Slope Form to Standard and Slope-int

• We gotta do it, so lets try it out for this equation.

• First standard Form20 7( 10)y x

7 90y x

20 7 70y x -20 -20

-7x -7x

7 90x y

Time out!

It’s Slope-int!

It’s Standard!

Wow we WOW WOW!

Let’s keep on truckin’

Last Example using 2 points!

• Using (3,-6) and (-5,2), find the equation of the line using point-slope form.

• We need to find m Wait a minute, We’ve Done This!!

2 1

2 1

( ) ( 5 ( 6)) ( 5 6)( ) (2 3) (2 3)y ymx x

( 5 6) 1 1(2 3) 1

Last Example using 2 points!• Using (3,-6) and (-5,2), find the equation of the

line using point-slope form.• m = -1• So lets plug and chug, but which points? • They both work!!!

1 1( )y y m x x

( 6) 1( 3)y x 1 1( )y y m x x

(3,-6) (-5,2)

6 1( 3)y x

( 5) 1( 2)y x

5 1( 2)y x They Look Different, But They describe the same Line.

Don’t Believe me? Find the x and y-int!!