1. Graph the following ordered pairs on the same coordinate plane:
Warm-up 2/25/08
Graph the following ordered pairs on the same coordinate plane:
A (0,1)
B (2,3)
C (-1,2)
D (-1,-1)

2. Warm-up 2/9/07 7c + 2 = -37 -5.5714 -2c -8 = 12 -10 2/3c + 11 = 5 -9
Solve each equation for c.
7c + 2 = -37
-2c -8 = 12
2/3c + 11 = 5
c/-4 = 9/3
30% of c = 120
c% of 90 = 150
-10 -9
-12
400
166.7

3. 30 MINUTES TO FINISH TESTS
REMINDERS
I WILL BE OUT TOMORROW, YOU WILL HAVE SOME REVIEW WORKSHEETS THAT WILL BE FOR A GRADE
30 MINUTES TO FINISH TESTS
IF YOU DON’T FINISH TEST, YOU WILL NEED TO COME BACK DURING LUNCH OR AFTER SCHOOL WEDNESDAY

4. GRAPHING AND WRITING LINEAR EQUATIONS
Unit 5
GRAPHING AND WRITING LINEAR EQUATIONS
UNIT 5 PROJECT

5. Topic:
Graphing and Writing Linear Equations
Key Learning(s):
Find slope, graph lines using a variety of methods, write equations of lines
Unit Essential Question (UEQ):
How do you find the slope of a line? How do you write an equation of any given line?

6. Concept I:
Slope and Rate of Change (5.1, 5.2)
Lesson Essential Question:
How do you calculate the slope of a line?
How do you draw a line through a point with a given slope?
How do you find rates of change from tables and graphs?
Vocabulary:
Slope, rate of change, linear function

7. Slope-Intercept form (5.4)
Concept II:
Slope-Intercept form (5.4)
Lesson Essential Question (LEQ):
How do you use slope and the y-intercept to draw graphs and write equations?
Vocabulary:
Y-intercept
Slope-intercept form

8. Concept III:
Writing the equation of a line
Lesson Essential Question (LEQ):
How do you write an equation given the slope and a point?
How do you write an equation given two points from a graph or a table?
Vocabulary:

9. Concept IV:
Using the x-intercept
Lesson Essential Question (LEQ):
How do you graph equations using the x-and y-intercepts?
How do you write equations in standard form?
How do you use the x-intercept of a linear equation to solve a related one-variable equation?
Vocabulary:
X-intercept; point-slope form; break-even point

10. Concept V:
Parallel and Perpendicular Lines
Lesson Essential Question (LEQ):
How do you write equations for parallel and perpendicular lines?
How do you use slope to determine if two lines are parallel, perpendicular, or neither?
Vocabulary:
Parallel lines, perpendicular lines

11. Concept VI:
Direct & Inverse Variation (5.3)
Lesson Essential Question (LEQ):
How do you relate slope to constant of variation?
How do you solve inverse variations?
How does direct variation compare to inverse variation?
Vocabulary:
Linear equation; constant of variation; direct variation; inverse variation

12. Concept VII:
Scatter Plots and Equations of Lines
Lesson Essential Question (LEQ):
How do you find the equation of a trend line?
How can you use a calculator to find the line of best fit?
Vocabulary:
Line of best fit, correlation coefficient

13. §5.1: Slope EQ: How do you calculate the slope of a given line?
What are some things that have slope?
The slope of a line is the measure of its steepness or “tilt”

14. 6 line2 5 line4 4 line3 3 2 1 line1 -6 -5 -4 -3 -2 -1
Imagine each of these lines is a hill. Which one has the least slope? (line 1) This line has a slope of zero. (it’s flat)
Line 2 is like the edge of a cliff. It has an undefined slope. X = 0 is undefined.
Line 3 has a steep slope, but not too bad. This line is y = x. All the y and x values are the same.
Which lines do you think have positive slopes? Negative?
Think about a car, driving left to right on the page. If it goes up hill, the line has a positive slope.
If it goes down hill, the line has a negative slope.

15. The slope of a line is given as a ratio of the rise to the run.
To find the slope of a line, you need to find two points on the line. Imagine yourself walking from one point to the other. (left to right).
You cannot count diagonally, you must go up or down, then across.
Then, write the slope as a ratio (fraction).

16. 6 5 4 3 A 2 1 -6 -5 -4 -3 -2 -1 D
Slope of line AD is 6/5. It is positive.

17. 6 5 4 A 3 2 B 1 -6 -5 -4 -3 -2 -1
When finding the slope of a line, look for two points where the line crosses two lines (to make it easy). Draw two points, then find the slope between those two points.
THE SLOPE OF LINE AB IS -2/2 = -1.
THE SLOPE OF THIS LINE IS NEGATIVE (-1). THIS MAKES SENSE BECAUSE IT GOES DOWNHILL.

18. A surveyor places two stakes, A and B, on the side of a hill
A surveyor places two stakes, A and B, on the side of a hill. Stake A is 20 feet lower than stake B. If the horizontal distance between the two stakes is 200 feet, what is the slope of the hill?
Draw a diagram.
Slope = 20/200 = 1/10 or 0.1

19. Slope Formula
There is a formula to find the slope of two points without having to graph a line.
If you have two points, A and B, we will name the coordinates for A(x1,y1) and the coordinates for B(x2,y2) to distinguish between the two points.
The formula:
slope of AB = y2 – y1
x2 – x1

20. This slope formula is just finding
the difference in the y-coordinates rise
the difference in the x-coordinates run
Ex. Find the slope between point A(-2,-3) and B(1,4).
*Make sure you subtract them in the same order!
Formula: -3 – 4 = -7 = 7
-2 –

21. Given a point and slope Graph the point
Count the slope from that point
Find your 2nd point
Draw the line
Ex) Draw a line through the point (1,2) with slope -1/2.

22. Find slope and equation
To find the equation of a line given two points
Find the slope
Determine what the line is
Y = vs. x =
Ex) Find the slope & equation between (1,2) and (4,2).
Ex) Find the slope & equation between
(4,-1) and (4,2)

23. Section 5.1 p.217 – 218 #1 – 15 odd 18 – 21 all 25 – 33 odd
Assignment
Section 5.1 p.217 – 218 #1 – 15 odd 18 – 21 all 25 – 33 odd

24. Warm-up 2/27/08
In your textbooks, read over p. 219 on changing between units (dimensional analysis) and do # 1 – 12.

25. 5.2: Rates of change
How do you find rates of change from tables and graphs? Rate of change (slope) How do you find slope? How do you find the rate of change? Linear function

26. 5.4: Slope-Intercept Form
LEQ: How do you use slope and the y-intercept to draw graphs and write equations? Slope intercept form Y = mx + b “m” is the slope “b” is the y-intercept (where it crosses the “y-axis”)

27. How to graph them Put the “y-intercept” point on the y-axis
From that point…
Count the slope to find another point (or two)
Draw the line connecting the points.

28. Changing an equation to slope intercept form:
In order to use an equation in slope-intercept form, you must ensure that it is first IN slope intercept form.
If it is not:
Solve the equation so that “y” is by itself on one side
Everything else on the other side can be combined/rearranged to mx + b form.

29. Steps: Re-write the equation in “function” form
Identify the y-intercept
Graph the y-intercept
Identify the slope
Use slope to plot more points
Draw the line through the points

30. Section 5.2 p. 222 – 223 # 1 – 21 odd Section 5.4 p. 233 #1 – 23 odd
Assignment
Section 5.2 p. 222 – 223 # 1 – 21 odd Section 5.4 p. 233 #1 – 23 odd

31. Warm-up 2/28/08
Find the slope of the line passing through (-2,-3) and (3, -1/2).
Graph a line with a slope of -1/2 which passes through the point (2,1).

32. Return Papers Go over 5.1, 5.2, 5.4 Questions?

33. 5.1 Quiz

34. §5.5: Writing Equations of Lines
LEQ: Given various points, how can you find the equation of a line? Your friend called you one night with a question about her algebra homework. You decide that the best way to help her is to have her draw the line of an equation on a graph. How would you describe the line without actually showing her?

35. Graphic Organizer Worksheet 5.5
Practice!
Graphic Organizer Worksheet 5.5

36. Summary On a piece of scratch paper:
Write an equation of a line through point (-3, -1) with a slope of -2.
Write an equation for the line that passes through point (-3,2) and (3,1)
Decide if the following relationship between the x- and y-values is linear.
If it is, write an equation for the relationship.

37. Homework
Section 5.5 p. 239 # 1 – 39 odd

38. Warm-up 2/29/08 Write the equation of the line.

39. Write the equation of the line:

40. Write the equation of the line:

41. Check HW (answers) Finish 5.5 WS 5.5 Summary

42. Checkpoint 1 Unit 5 project Due Date: Tuesday, March 11

43. How do you put a table into a calculator and graph it? p. 240 in book

44. 5.6: Scatter plots and equations of lines
LEQ: Given various points, how do you find the equation of a line? Scatter plots Correlation Positive Negative None Correlation Coefficient

45. p. 243 – 244 #1 – 6, 8 – 10, 12 Do #12 by hand Assignment p. 244 #11
Practice
p. 243 – 244 #1 – 6, 8 – 10, 12 Do #12 by hand Assignment p. 244 #11

46. Warm-up 3/3/08
Write the equation of the line with given slope and y-intercept:
M = ¾ ; b = 8
M = -7; b = ½
Write the equation of the line through the given points
(4,3) (-2,1)
(5,-4) (0,2)

47. Quiz?

48. §5-7: Standard Form 5.9: Using x-intercepts
LEQ: What requirements does the standard form of an equation have? In the slope intercept of an equation: Y is the M is the B is the

49. Standard form Standard form of an equation is in the form:
Ax + By = C
Basically the x and y-terms are on one side of the equation and the number term is on the other sides of the equation.
It is called standard form because it is most often used.

50. Using standard form to graph equations
Standard form can be used to easily graph equations using the x- and y-intercepts
Do not try to use the method of x- and y-intercepts unless the equation is in standard form!
“cover up” method
reasoning

51. Find the x- and y-intercepts then graph each equation
5x + 2y = 10
6.5x – 4y = 52
-x + 3y = -15
8x – y = 104
2; 5
8; -13
15; -5
13; -104

52. Break-even point
When starting a business, people want to know their break even point
The break even point is the point at which their income equals their expenses
Suppose you invested $140 to start a business selling T-shirts. You sell each shirt for $ Find the break even point.
IE) When does 7.50t = 140?
How many t-shirts must you sell?

53. Guided Practice
In Textbooks p. 248 – 249 #12, 14, 24 – 30 Even, 32

54. Assignment
Section 5.7 p. 248 – 249 # 1 – 11 odd #15 – 31 odd On 15 – 21, only find the intercepts

55. Warm-up 3/4/08 Change each equation to Ax + By = C form. Y = 5x – 1
Write the equation of the line thru the points.
(1, -4),(7,0)
(1/2, -4),(-11, -4)

56. Heads up
Throughout the next month, there will be various visitors in the room
Behavior
Questions
3rd block mid-terms will be next Tuesday, so START STUDYING NOW!
No late work will be accepted more than 2 weeks after the original due date unless there are special circumstances.

57. Any 5.7 Homework Questions?

58. How do you know if a given point is on a line?
Ex. Does the point (5,2) lie on the line given by the equation x + y = 7?
To determine if the point is on the line, put the x-value from the ordered pair in for x and the y-value into for y and solve. If the equation is true, the point is on the line.
x + y = 7
(5) + (2) = 7? Yes.
So, this point does lie on the line given.

59. Assignment
Section 5.9 p. 258 – 259 #4 – 6, 11 – 21

60. §5.8: Parallel & Perpendicular Lines
LEQ: What is true about all parallel and perpendicular lines? What does it mean to be parallel? What does it mean to be perpendicular?

61. Parallel or Perpendicular?
2x + y = 15 3y = -6x + 30 How do you know?

62. Parallel or Perpendicular?
Y = 4x + 3/4 Y = -1/4x + 4 How do you know?

63. Generalization Parallel lines Perpendicular lines
Have the exact same slope, but a different y-intercept
Perpendicular lines
Have opposite, reciprocal slopes
Y-intercept can be same or different

64. Find the slope of a line parallel to the equation
Y = -2/3x – 1
2x – 3y = -2
X = 5
X = 0
7x + 2y = 12
-2/3
2/3
Undef.
-7/2

65. Y = -3x Y = x Y = -x/5 – 7 X = 3 3x + 5y = 7 Y = 0.25x 1/3 -1 5 5/3 -4
Find the slope of the line perpendicular to the graph of each equation.
Y = -3x
Y = x
Y = -x/5 – 7
X = 3
3x + 5y = 7
Y = 0.25x
1/3 -1 5
5/3 -4

66. Practice
Guided Practice p. 254 # 42 – 46 even
Assignment p. 253 – 254 #1 – 30 (mult of 3), – 49 odd

67. Warm-up 3/5/08
For each equation, write the equation of a line that is perpendicular and one that is parallel to the given line.
Y = 3x – 2
4x + 5y = 10
Y = 2/3x + 1/6
Y = 1.6x - 0.4

68. Last quick section:

69. §5.3: Direct Variation
EQ: What is consistent in direct variation equations? How are they related to linear functions?
If a relationship can be expressed in the form
y = kx, the two variables are said to vary directly, or be proportional.
(They increase or decrease together)

70. k is the constant of variation -rate of change (y’s divided by x’s)
y = kx
k is the constant of variation
-rate of change (y’s divided by x’s)
-slope of the graphed line
*NOTE: the y-intercept is 0.
Direct variation –
A linear function that can be written in the form y = kx where k≠0.
Complete p.64 #5a, b, c
Complete #65 #6

71. Relationships among linear equations
2y = x – 1 x + y = 7
3y = 5 Linear Equations 3x + 2y = 6
X = 3
Linear Equations in
Function form Y = -5x - 2
Is a direct variation always a linear function?
Under what circumstances, if any, would a linear function be a direct variation?
Direct Variation
f(x) = -3x

78. Identify the Slope

79. Identify the Slope

80. Identify the Slope

81. Identify the Slope

82. Identify the Slope

83. Write the equation of a direct variation that passes through the point

84. Write the equation of a direct variation that passes through the point

85. Write the equation of a direct variation that passes through the point

86. Write the equation of a direct variation that passes through the point

87. Write the equation of a direct variation that passes through the point

88. Multiply to find the missing value Include units in the answer

89. Multiply to find the missing value Include units in the answer

90. Multiply to find the missing value Include units in the answer

91. IN CLASS Test Review

92. Homework
Wrap up
p. 261 – 263 #

93. WARM-UP 3/6/08
Provide a step-by step procedure of how each method works.
Slope and y-intercept
Slope and a point
Two points
Using x and y-intercept
Ax + By = C form
What is a real world situation that can be modeled with a linear equation.

94. Reminders Test Review Warm-ups I’ll be out tomorrow
You will have practice mid-term to work on
Take it seriously
I will grade them over the weekend and try to give you feedback on Monday.

95. Warm-up 3/10/08
A line goes through (1,3) and has slope 3/2. Graph the line.
What is true about a line that rises as it goes from left to right?
What would a direct variation with a constant of variation of 2/3 look like?
What are the x- and y-intercepts of the line 8x + 4y = 4.

96. Reminder: Mid-term TOMORROW!!!
Agenda
Reminder: Mid-term TOMORROW!!!
Pass back unit 5 tests
Go over unit 5 tests
Re-takes
Study for mid-term!