alg. 1 day 60 6 4 point slope form
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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
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- y y 1 = m ( - x x 1)C O P Y