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