1. Midterm Review

2. Reviewing Linear Equations

3. Finding the Slope Given a graph how do I find the slope?
Find the Slope of the following graphs

4. Finding the Slope Find the Slope of the following graphs
What about the slope of these graphs?

5. Finding the Slope What is the formula for finding the slope?
Find the slope of the line through the given points.
(-1, 2) and (-5,10) (-7, 10 ) and (1, 10)
3. (1,3) and (0,-9) (3, 7) and (3, -8)

6. Direct Variation

7. Direct Variation
Direct Variation: the relationship that can be represented by a function if the form:
y = kx
Constant of variation: the constant variable K is the coefficient of x on the y=kx equation.

8. Identifying a Direct Variation: If the equation can be written in y = kx we have a direct variation.
Ex:
Does the equation represent a direct variation?
a) 7y = 2x b) 3y + 4x = 8

9. Writing a direct variation equation
Suppose y varies directly with x, and y = 35 when x = 5. Write a direct variation equation. Then find y when x = 9.

10. Writing a direct variation equation
Suppose y varies directly with x, and y = 10 when x = -2. Write a direct variation equation. Then find y when x = -15.

12. Writing a direct variation from a table
For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

13. Writing a direct variation from a table
For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

14. Graphing Linear Equations
Graph the following linear equation. Y = 𝟏 𝟐 𝒙 + 3
What form of linear equation should be used to graph?
What are our steps to graph a linear equation?

15. Graphing Linear Equations
Graph the following linear equation. Y = -2𝒙 + 1

16. Changing Forms
For practice, change the following equations to the slope-intercept form:
6x + y = y = 8x
2y = 6x – x – 2y = 12
What is the standard form of a linear equation?
What are the special restrictions that go along with the standard form?

17. Changing Forms What is the point-slope form of a linear equation?
Change the following to standard form.
y – 5 = -1/2 (x – 3) y – 3 = ½(x + 6)

18. Writing Equations
Write the equation given a point and the slope in point-slope form. Point: (-7, 2) Slope: 3

19. Writing Equations
Write the equation of a line given two points. (-8, 3) (-4, 4)

20. Parallel & Perpendicular Lines

21. Parallel Lines Parallel Lines - lines that never intersect
What is the slope of the
red line?
1/2
blue line?
Parallel Lines have the slope!
same

22. Parallel Lines
Determine if the lines are parallel
yes

23. Equations of Parallel Lines
Write an equation for the line that contains (5, 1) and is parallel to
m =

24. Equations of Parallel Lines
Write an equation for the line that contains (2, -6) and is parallel to
m = 3
y + 6 = 3(x – 2)

25. Perpendicular Lines
Perpendicular Lines – lines that intersect to form right angles
What is the slope of the
red line?
-1/4
blue line?
4/1
Perpendicular Lines have slope!
opposite reciprocal

26. Perpendicular Lines What is the slope of the perpendicular line? 7.
-5/2 8.
5/1 = 5 9.
1/2

27. Equations of Perpendicular Lines
Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3
m =

28. Equations of Perpendicular Lines
Find the equation of the line that contains (2, -3) and is perpendicular to
m = 2
y + 3 = 2(x – 2)

29. Challenge What is the slope of the line that is parallel to x = 4?
undefined
What is the slope of the line that is perpendicular to x = 4?
zero

30. Arithmetic Sequences

31. An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

32. The common difference is the amount it increase or decreases by each time.

33. Formula for the nth term of an ARITHMETIC sequence.

34. Arithmetic sequences
The sequence below shows the total number of days Francisco had used his gym membership at the end of weeks 1, 2, 3, and 4. Assuming the pattern below continued, which function (equation) could be used to find the total number of days Francisco had used his gym membership at the end of week n?
5, 10, 15, 20…

35. Arithmetic sequences Consider the following arithmetic sequence:
6, 11, 16, 21… What is the value of the 23rd term?

36. Determine the explicit formula for the following

37. Scatterplots & Trend Lines

38. DETERMINING THE CORRELATION OF X AND Y
TYPES OF CORRELATION
Positive Correlation
Negative Correlation
No Correlation

39. Scatter plots provide a convenient way to determine whether a ___________ exists between two variables.
correlation
positive
A __________ correlation occurs when both variables increase.
negative
A ___________ correlation occurs when one variable increases and the other variable decreases.
If the data points are randomly scattered there is _______ or no correlation.
little

40. Determine the Correlation
Write increase or decrease to complete the sentence regarding expectations for the situation.
The more one studies, their grades will _____.
The more a person diets, their weight will ______,
The longer one diets, the amount of weight loss will ______.
The more a person exercises, their muscle mass will _____.
The more a person exercises, their fat mass will ______.
The more a person jumps rope, their heart rate will _____.
The more a class talks, the teacher’s patience will _____.
The more a person reads, their vocabulary will _____.
This is called correlation.

41. Line of Best Fit
line of best fit - The trend line that shows the relationship between two sets of data most
A graphing calculator computes the equation of a line of best fit using a method called linear regression.
The graphing calculator gives you the correlation coefficient r.
negative
correlation no
correlation
positive
correlation

42. Finding the Equation of Line of Best Fit
Example 1: Find an equation for the trend line and the correlation coefficient. Estimate the number of calories in a fast- food that has 14g of fat. Show a scatter plot for the given data.
Calories and Fat in Selected Fast-Food Meals
Fat(g) 6 7 10 19 20 27 36
Calories
276
260
220
388
430
550
633
Solution:
Use your graphing calculator to find the line of best fit and the correlation coefficient.

43. Cont (example 1)...
Step 2. Use the CALC feature in the STAT screen. Find the equation for the line of best fit  LinReg (ax + b)
LinReg
y = ax + b
a =
b =
r2 =
r =
Slope
y-intercept
Correlation coefficient
The equation for the line of best fit is y = 13.61x and the correlation coefficient r is

44. Finding the Equation of Line of Best Fit
Recreation Expenditures
Example 2. Use a graphing calculator to find the equation of the line of best fit for the data at the right. What is the correlation coefficient? Estimate the recreation expenditures in 2010.
Year
Dollars (Billions)
1993
340
1994
369
1995
402
1996
430
1997
457
1998
489
1999
527
2000
574
Answers:
y = 32.33x
r =
The expenditures in 2010 will be 885 billions
Let 1993 = 93

45. Do these… Use a graphing calculator to find the equation of line of best fit for the data. Find the value of the correlation coefficient r.
3. Use the equation to predict the time needed to travel 32 miles on a bicycle. How many miles will he travel for 125 mins.
Speed on a Bicycle Trip
Miles 5 10 14 18 22
Time (min) 27 46 71 78
107
Answers: y = 4.56x
r. =
about min or 149 min
26.77 or 27 miles.

46. Systems of Equations

47. Solve by graphing
𝑦= 2 3 𝑥+ 2 3
𝑦=−4𝑥+24

48. Solve by substitution
2𝑥−3𝑦=−2
𝑦=−4𝑥+24

49. Solve by elimination
4𝑥−3𝑦=25
−3𝑥+8𝑦=10

50. Systems of Inequalities

52. Write the following system of inequalities
Answer:

53. Write the following system of inequalities
Answer:

54. Exponent Rules

55. Let’s Try Some More Complicated Problems

56. Let’s Try Some More Complicated Problems

57. Let’s Try Some More Complicated Problems

58. Let’s Try Some More Complicated Problems

59. Let’s Try Some More Complicated Problems

60. Let’s Try Some More Complicated Problems

61. Let’s Try Some More Complicated Problems

62. Let’s Try Some More Complicated Problems

63. Find the Area

64. Find the area of the triangle?

65. Polynomials

66. Polynomials
Write each polynomial in standard form. Then name each polynomial based on degree and number of terms.
1. 4x + x2  w + 3  2w + 8w3

67. Adding Polynomials You can add polynomials by adding like terms
Ex. (x2 + 3x  2) + (4x2  5x + 2)
Identify the like terms
There are two Methods. You can add Vertically or Horizontally
Let’s try both ways

68. Subtracting Polynomials
Recall that subtraction means to add the opposite. So when you subtract a polynomial, change each of the terms to its opposite. Then add the coefficients.
Let’s Try an example
Ex. (8t2 + t + 10)  (9t2  9t  1)

69. More Practice!!!! (5x3 + 3x2  7x + 10)  (3x3  x2 + 4x  1)
(4m3 + 7m  4) + (2m3  6m + 8)
(7c3 + c2  8c  11)  (3c3 + 2c2 + c  4)

70. More Practice
Find the Perimeter
𝒙 𝟐 +𝟐
6x - 3
x + 12
8x-1
𝒙 𝟐 −𝒙

71. Multiplying Polynomials
Let’s try multiplying a monomial and a trinomial!
Practice 1: –3c (8 + 2c – c 3)
Practice 2: 8a 2 (–a 7 + 7a – 7)

72. Multiplying Binomials
Ex. (2x +1)(x + 2)
Box Method F.O.I.L Method

73. Practice Simplify each product (Use any method) 1. (x + 3)(x + 8)
3. (5h – 3)(h + 7)

74. More Practice
Find the Area
𝒙 𝟐 +𝟐
6x - 3
8x-1

75. Factoring

76. Factor out the GCF

77. Factor out the GCF

81. Factoring the Difference of Squares

82. Factoring the Difference of Squares

86. Factoring when a = 1

87. Factoring when a = 1 *Don’t forget to check for a GCF

88. Factoring when a>1

89. Factoring Perfect Square Trinomials

90. Factoring Perfect Square Trinomials

91. Factoring by Grouping
Ex:

92. Factoring by Grouping
Ex2:

93. You Try!

94. Answers