Review Homework Page 9-10 11)(1:05, 4000), (1:15, 2600) Slope = 2600-4000 = -1400 = -140 75-65 10...
-
Upload
archibald-mcdaniel -
Category
Documents
-
view
216 -
download
0
description
Transcript of Review Homework Page 9-10 11)(1:05, 4000), (1:15, 2600) Slope = 2600-4000 = -1400 = -140 75-65 10...
Review Homework Page 9-10
11)(1:05, 4000), (1:15, 2600)
Slope = 2600-4000 = -1400 = -140 75-65 10-140 meters per minute-8400 meters per hour
1-1 Equations of Lines1-1 Equations of Lines
Slope ( 기울기 ) formula
m y2 y1
x2 x1
We can use this formula to determine the equations of lines. All equations will have the variables y and x and values for any remaining term
Slope Intercept Form page 12
y mx b
x
y
x 0
y b
x,y
Any point on the line
m y bx 0
m y bx
mx y b
0,b
y-intercept
a a a a
y = ax + ba = slope b= y-intercept
Examplesy = 3x -2y = - ½ x + ¼ y = 2
All values except for x and y and replaced
Determine the slope ( 기울기 ) and y-intercept (y- 절편 )of the
following
1 y x 1
(2) 3x 4y 8
a = -1b = 1
Graph y=3x+1
4
2
-2
-4
-10 -5 5 10
y-intercept b=1
Draw a line through the points
Practice page 13-14
• 1) y=6x+4000• 2a) y = 3x• 2b) y= -2x -1• 3) y=200 – 50t• 4) rate of speed (- sign shows direction)• 5) Time (t) 1 2 3 4
km (y) 150 100 50 0
Point Slope Form page 18
y y1 m x x1
x
y
x x1
y y1
x,y
Any point on the line
m y y1x x1
m x x1 y y1
x1,y1
Any point on the line
a a a
Point Slope Form page 18
Examples
y – 3 = 2(x + 1)y + 5 = ½(x – ¼ )
All values except for x and y and replaced
1 6,9 and 2, 1
2 2,1 and 2, 1
y – 9 = 2.5(x - 6) ory + 1 = 2.5(x - 2)
y – 1 = - ½ (x + 2) ory + 1 = - ½ (x – 2)
Graphing Point Slope y-3=2(x+1)
4
2
-2
-4
-10 -5 5 10
plot the point (-1,3)
Draw a line through the points
Practice page 20-21 #1,2,3,61)y-4=-4(x+2)2)y= -4x -43)Any of the following
y-4=-1(x+2), y-3=-1(x+1), y-2=-1(x) , y=-1(x-2), y+1=-1(x-3)
4)y=-2x5)y=4x+36)y=-3x+7
Standard Form page 25
Ax + By = CA≥0,A and B can not both be 0.Most of the time it is written with integer coefficients ( 정수계수 ) A,B,C ∈ℤ
Standard Form
Examples
3x + 4y = 6
5x – 11y = 22
All values except for x and y and replaced
Using Standard Form to Find Intercepts
Practice page 27
1)2x+y=32)4x+y=53)3x+2y=44)2x-3y=185)horizontal y=-4 vertical x=26)4x+y=4
General Form
Some textbooks refer to it as standard form since non-linear relations use this as standard form.
Ax + By + C = 0
General Form
Examples
3x – 4y + 2 = 0
x + 2y – 3 = 0
Formulas of Lines
m y2 y1
x2 x1
Slope Formula
y mx b Slope Intercept Form
y y1 m x x1 Point Slope Form
Ax + By = C Standard FormA,B,C ∈ℤ, A ≥ 0Ax + By + C = 0 General Form
a
a
a
Changing forms
To change to standard form, simplify and then get x and y on one side of the equation and the constant on the other. Ax+By=C A≥0, A,B,C∈ℤTo change to slope intercept, form, simplify and get y alone on one side of the equation.
Homework
•Pages 15-17, 22-23, 28