1. CH 1.1: Linear Equations

2. 1) Grab a computer & login
Warm Up
1) Grab a computer & login
2) Go to student.desmos.com and type in the class code. You may choose to log in with google or sign in without an account. (if you sign in with google, your work will be saved if the internet accidentally logs you out
3) Please type your name in as your firstname & last initial. You are getting points for this assignment so I need to know who you are.
4) Keep in mind, I can see everything you type in. I know you will all be appropriate and kind.
5) Have fun!
Other options:
Polygraph
“land the plane”

3. What is slope?
Slope is a measure of steepness. The slope of a non-vertical line represents the number of units the line rises or falls vertically for each unit of horizontal change from left to right. The formula for the slope of a line Passing through the points ( 𝑥 1 , 𝑦 1 ) and ( 𝑥 2 , 𝑦 2 ) is

4. 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

5. EX 1: How can I find the slope between two points?
Find the slope between (-2, 5) and (4, -3)
DRAW PIC ON WHITEBOARD (They should put in column

6. You Try! b) Find the slope between (3, 4) and (3,1)

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

10. A) Find the coordinates of point A.
B) Find the slope of the line between (1,2) and (7,5)

11. cont
C) Using the same process as before, find an expression for the slope using the points (1,2) and (x,y). Fill in the boxes for the expressions for the two sides of the slope triangle.
D) Since the slope between (x,y) and (1,2) equals the slope between (7,5) and (1,2), let the answer your found in B) equal the results found in C). Then multiply both sides by (x-1). The final expression is the point slope form of the line.

12. We have 3 main ways of classifying lines…
Point- Slope Form B) Slope-Intercept Form C)General/Standard Form
y = mx + b.
Ax + By + C = 0

13. Core Concept: The Point Slope Form of the Equation of a line
The point-slope form of the equation of a line is It is best used when you have one point and the slope
Start with lope and show the multiplication
EX 1: Find an equation of the line having a slope of -2 and passing through (1,5)

14. You Try!
Find an equation of the line having a slope of 3 and passing through (1,-2)

15. EX 2: During 2004, Nike’s net sales were $12
EX 2: 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 bill in 2006
Slope = 1.49 billion each year
So bill in 2006

16. The Meaning of Slope HW
Due next class Use complete sentences/phrases Make detailed pictures when asked

17. Day 2

18. 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 Warm Up on the ch 1.1 continued noteguide

19. Slope Intercept form

20. EX 3: Graphing an equation of a line with slope intercept form
In EX 1, we were asked to find an equation of the line having a slope of -2 and passing through (1,5).
We got _____________ as the answer. Put in slope-intercept form. Then determine the slope, y-intercept, and graph.
Steps in Graphing
1) Plot y-int
2) Use Slope to find next point

21. 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 m = 0, b = 5
y = -4x + 3
y = 5 – x
8x + y =
y = x
y = 5
Call outs

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

23. HW Day 2 Practice With Plotting Lines and slope

24. Matching Game!

25. How did you decide which cards to group with this card
How did you decide which cards to group with this card? What feature(s) were important to you?

26. 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?

27. What is special about parallel lines?
 What is special about perpendicular lines?
𝒎 𝟏 = 𝒎 𝟐
two lines with the same slopes
𝒎 𝟏 =− 𝟏 𝒎 𝟐
two lines with negative reciprocal slopes
EX 4: 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

28. You Try!
Find the slope-intercept form of the equation of a line that passes through the point (2, -1) and is parallel to the line 2x – 3y = 5

29. The Sorting Game
Each student will receive a list of paired lines. With your partners, work 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!

30. Parallel
Perpendicular
Neither

31. Review
Can graph whichever 3 they choose in notebook?

32. HW Guidelines

33. HW
Pg 11 # 1, odd, 33, 43, 53, 55, 57, 63, 65, 75