D O N O W

1 . , F r o m y o u r n o t e s o r y o u r m e m o r y w r it e t h e f o r m u la f o r 2 .t h e s lo p e o f a lin e w h e n y o u h a v e p o in t s

2 . 2 .W r it e d o w n m e t h o d s w e h a v e u s e d t o g r a p h a lin e

3 . = + .y m x b = 3 + 1 , ? ?If y x w h a t is m W h a t is b

4 . + = .A x B y C 3 - 4 = 7 , ? ? ?If x y w h a t is B A C

5 . - y y 1 = ( - m x x 1). - 6 = 3 ( - 2 ), If y x w h a t is x 1? y 1? ?m

Agenda Monday, Dec. 6

Do No

Homework Check

homework 16  p. 307 # 2 ­ 18 evens

Point Slope form

6­4 Ex. 1 & 2 

Point-Slope Form of Linear Equations

Suppose you know that a line passes through the point (3,4) with a slope of 2. You can quickly write an equation of the line using point-slope form.

(y - y1 ) = m(x - x1)(x1, y1) is a point on the line and m is the slope.

So the difference in y equals the slope times the difference in x.

m = (y - y 1 ) (x - x1)

- P O IN T S L O P E F O R M

m = y 2 - y 1 x 2 - x 1

- y y 1 = m ( - x x 1)

- y 5 = ¾ ( - x 1 )

= (1 , 5 )P o in t = S lo p e¾

(x 2 - x 1) (x 2 - x 1)m = y 2 - y 1 x 2 - x 1

Graphing Using Point-Slope form

Graph the equation (y - 1) = 2/3(x - 3).

The equation shows that the line passes through the point (3, 1) with a slope of 2/3. Start at (3, 1), go up 2 units and right 3 units. Draw your line.

Now you tryGraph the equation y - 4 = 2(x - 3)

Start at (3, 4) go up 2 and right 1.

- y y 1 = m ( - x x 1)

, F r o m e a c h e q u a t io n n a m e t h e s lo p e a n d a p o in t . o n t h e lin e

y - 4 = 3/2(x - 1) 3/2 (1, 4)

y - 2 = 3(x - 5) 3 (5, 2)

y - 6 = x - 6 1(6, 6)

y + 2 = -3(x + 4) -3 (-4, -2)

y - 1 = 1/2(x + 1/2) 1/2(-1/2, 1)

y + 6 = x 1(0, -6)

mmmmmm (x 1, y 1)(x 1, y 1)(x 1, y 1)(x 1, y 1)(x 1, y 1)(x 1, y 1)

Write an equation in point-slope form of the line that passes through the point (2, 5) and has a slope of 3.

(y - y1 ) = m(x - x1)

Substitute the 5 in for y1 , the 2 in for x1 and the 3 in for m.

y - 5 = 3(x - 2)

Now you try: Write the equation of the line with a slope of -3 that passes through the point (-1, 7) in point-slope form.

(y - 7) = -3(x + 1)

Write the equation of the line with a slope of 2/3 that passes through the point (10, -8).

y + 8 = 2/5(x - 10)

- W r it e a n e q u a t io n in p o in t s lo p e f o r m w h ic h g o e s ( ) .t h r o u g h t h e g iv e n p o in t s w it h t h e in f o r m a t io n g iv e n

m = 2

m = -3/2

m = 1/4

m = 1

pt. = (3, 5)

pt. = (4, 3)

pt. = (-4, -2)

pt. = (9, -1)

y - 5 = 2(x - 3)

y - 3 = -3/2(x - 4)

y + 2 = 1/4(x + 4)

y + 1 = x - 9

- y y 1 = m ( - x x 1)

- y y 1 = m ( - x x 1)

- y y 1 = m ( - x x 1) - y y 1 = m ( - x x 1) - y y 1 = m ( - x x 1)

Graph this equation:

y - 5 = 1/2 (x - 2)

y - y1 = m (x - x1)

Graph this equation:

y + 3 = 2(x + 1)

y - y1 = m (x - x1)

- P o in t S lo p e F o r m Th in g s t oR e m e m b e r

· ' .It s ju s t a lin e a r e q u a t io n in a d if f e r e n t f o r m a t·· , .W h e n g iv e n s lo p e a n d a p o in t p lu g t h e m b o t h in·· .W a t c h o u t f o r n e g a t iv e s·· 2 , , W h e n g iv e n p o in t s f in d s lo p e t h e n u s e t h a t s lo p e a n d

.e it h e r p o in t·· - , .O n c e y o u u s e p o in t s lo p e y o u c a n c h a n g e t o o t h e r f o r m s

- y y 1 = m ( - x x 1)C O P Y