Review Homework Page )(1:05, 4000), (1:15, 2600) Slope = = = meters per minute meters per hour

1-1 Equations of Lines 1-1 Equations of Lines

Slope ( 기울기 ) formula 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 x y Any point on the line y-intercept a a a a

y = ax + b a = slope b= y-intercept Examples y = 3x -2 y = - 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 a = -1 b = 1

Graph y=3x+1 y-intercept b=1 Draw a line through the points

Practice page ) y=6x a) y = 3x 2b) y= -2x -1 3) y=200 – 50t 4) rate of speed (- sign shows direction) 5) Time (t)1234 km (y)

Point Slope Form page 18 x y 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

y – 9 = 2.5(x - 6) or y + 1 = 2.5(x - 2) y – 1 = - ½ (x + 2) or y + 1 = - ½ (x – 2)

Graphing Point Slope y-3=2(x+1) plot the point (-1,3) Draw a line through the points

Practice page #1,2,3,6 1)y-4=-4(x+2) 2)y= -4x -4 3)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=-2x 5)y=4x+3 6)y=-3x+7

Standard Form page 25 Ax + By = C A≥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=3 2)4x+y=5 3)3x+2y=4 4)2x-3y=18 5)horizontal y=-4 vertical x=2 6)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 Slope Formula Slope Intercept Form Point Slope Form Ax + By = C Standard Form A,B,C ∈ℤ, A ≥ 0 Ax + 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 ∈ℤ To change to slope intercept, form, simplify and get y alone on one side of the equation.

Homework Pages 15-17, 22-23, 28