CH 1.1: Linear Equations

Intro to Ch 1.1 Partner Questions 1)What is Steepness? Give an example of when you deal with it or notice it. 2)Which of the ramps is the steepest? Why? 3) How you would determine the steepest ramp from the following choices: Ramp A: width 40 mm, height 30 mm Ramp B: width 9mm, ramp length 54 mm Ramp C: ramp length 100mm, height 40 mm Ramp D: height 3cm, width 4cm Give each PAIR of student the half sheet of Paper to answer questions while you take role

*You are responsible for going back to this box and defining important words. Notebook checks will be random. Person with the closest birthday gets the notebooks.

*ORDER of subtraction is IMPORTANT DRAW PIC ON WHITEBOARD (They should put in column *ORDER of subtraction is IMPORTANT

m > 0 m < 0 m = 0 No m rises falls horizontal Vertical Write examples on board rises m > 0 falls m < 0 horizontal m = 0 Vertical No m

The Meaning of Slope Activity Work in your groups on each number. You will be presenting ideas periodically!

The Meaning of Slope HW Due next class

HW Questions? Review your homework briefly with your group members. Make corrections in another color. Then I will collect the homework for credit. Make a pile in the center when ready. When you are done, start the Practice With Equations of Lines review worksheet.

Practice With Plotting Lines and slope

We have 3 main ways of classifying lines… Point- Slope Form Slope-Intercept Form General/Standard Form

You have one point and the slope 𝒚− 𝒚 𝟏 = 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 (x− 𝒙 𝟏 ) Start with lope and show the multiplication *The idea here is to first find m with both points. Then, choose whichever point you want to substitute into the equation with the slope You have two points and no slope

(write in column next to EX 1) EX 1b: During 2004, Nike’s net sales were $12.25 billion, and in 2005 net sales were $13.74 billion. Assuming this trend is linear, predict the net sales for 2006. Slope = 1.49 billion each year So 15.23 bill in 2006

which kind of estimation? Linear interpolation Linear extrapolation DRAW PICTURE PG 6 Ex 1b was an example of which kind of estimation?

Redundant? Point- Slope Form Slope-Intercept Form F(x) = mx + b. line m b Point- Slope Form Slope-Intercept Form General/Standard Form F(x) = mx + b. Ax + By + C = 0

y = mx + b. Slope (0,b) Domain: (-inf, inf) Range: (-inf, inf)

Review of Slope-Intercept Form Name the slope and y-intercept of each equation: m = -4, b =3 m = - , b = 5 Rewrite as y = -8x m = -8, b = m = , b = 0 Rewrite as y = 0x + 5 m = 0, b = 5 y = -4x + 3 y = 5 – x 8x + y = y = x y = 5 Call outs

2) Use Slope to find next point 1) Plot y-int 2) Use Slope to find next point

x = - 4 b = 4 m = 0/1= 0 y = 0x + 4 y = 4 x y b = none m = 1/0= undefined x = - 4

*A and B are not BOTH zero Ax + By + C = 0 General *A and B are not BOTH zero form The viewing window might be different What can you conclude?

What does it mean for two lines to be Perpendicular? What does it mean for two lines to be Parallel? What does it mean for two lines to be Perpendicular? Have them write down what they think in their notebooks. Share with their partner. Then discuss. Where have you seen these in real life?

Aka negative reciprocal slopes 𝒎 𝟏 = 𝒎 𝟐 Aka same slopes 𝒎 𝟏 =− 𝟏 𝒎 𝟐 Aka negative reciprocal slopes EX 4a: Find the slope-intercept form of the equation of a line that passes through the point (2, -1) and is perpendicular to the line 2x – 3y = 5

Use a square viewing window, as in example below. Which one appears perpendicular?

The Sorting Game Each student will receive a list of paired lines. You and your partner will be working together to determine whether the lines are Parallel, Perpendicular, or Neither. Refer to these definitions in your notes if needed! Draw Parallel Perp Neither Table on Whiteboard . Have each group come up and write on of their equations up on the board. It must not already be written up there!

Parallel Perpendicular Neither

Journal #1:Productivity ASAP science What kinds of “study” techniques do you have/use currently in math classes? Why do those work? What does not work for you? After watching the ASAP Science video, what might you want to try out this year and why? Responses should be several sentences.

Goal Workshop (In Journal)

Exit Slip Can graph whichever 3 they choose in notebook?

HW Pg 11 # 1,2 11-19odd, 33, 43, 53, 55, 57, 63, 65, 75