1. Bell Ringer 10/8/14

2. Bell Ringer 10/9/14
Name the locations of the four quadrants on a graph.

3. Objective 1 The student will be able to:
graph ordered pairs on a coordinate plane.

4. Ordered pairs are used to locate points in a coordinate plane.
y-axis (vertical axis) 5 -5 5
x-axis (horizontal axis) -5
origin (0,0)

5. In an ordered pair, the first number is the x-coordinate
In an ordered pair, the first number is the x-coordinate. The second number is the y-coordinate. Graph. (-3, 2) 5 • -5 5 -5

6. What is the ordered pair for A?5
(3, 1)
(1, 3)
(-3, 1)
(3, -1)
• A -5 5 -5

7. What is the ordered pair for B?
(3, 2)
(-2, 3)
(-3, -2)
(3, -2) 5 -5 5
• B -5

8. What is the ordered pair for C?
(0, -4)
(-4, 0)
(0, 4)
(4, 0) 5 -5 5
• C -5

9. What is the ordered pair for D?
(-1, -6)
(-6, -1)
(-6, 1)
(6, -1) 5 -5 5
• D -5

10. Write the ordered pairs that name points A, B, C, and D.5
A = (1, 3)
B = (3, -2)
C = (0, -4)
D = (-6, -1)
• A -5 5
• D
• B
• C -5

11. The x-axis and y-axis separate the coordinate plane into four regions, called quadrants.II
(-, +) I
(+, +)
III
(-, -) IV
(+, -)

12. Name the quadrant in which each point is located (-5, 4)II
III IV
None – x-axis
None – y-axis

13. Name the quadrant in which each point is located (-2, -7)II
III IV
None – x-axis
None – y-axis

14. Name the quadrant in which each point is located (0, 3)II
III IV
None – x-axis
None – y-axis

15. HW

16. Linear Equations in Two Variables
Objective 2 and 3
Linear Equations in Two Variables
Students will complete a table for a linear equation and graph ordered pairs.

17. List some pairs of numbers that will satisfy the equation x + y = 4.
x = 1 and y = 3
x = 2 and y = 2
x = 4 and y = 0
What about negative numbers?
If x = -1 then y = ?
y = 5

18. x + y = 4 What about decimals? If x = 2.6 then y = ?
Now, let’s graph the pairs of numbers we have listed.

19. (1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4) • • • • •
Connect the points on your graph.
What does the graph look like?

20. It is a straight line! It is a linear relation.•
What does the line represent? • • • •
All solutions for the equation x+y=4!
Is (3, -1) a solution to this equation?
NO! You can check by graphing it or plugging into the equation!

21. 1) Which is a solution to 2x – y = 5?
(2, 1)
(3, 2)
(4, 3)
(5, 4)
Answer Now

22. 2) Which ordered pair is not a solution to the graph shown?
(0, -1)
(3, 5)
(-2, -5)
(-3, -1)
Answer Now

23. Bell Work 10/10/14
Write the following equation in standard form and check if the ordered pair (4 , 4) is a solution the linear equation:
3(y - 5) + 2(x + 2) = 10

24. Bell Ringer 10/13/14
For the linear equation -2x + 3y = 8, determine whether the ordered pair is a solution.
A. (-4 , 0)
B. (2 , -4)
2. Solve for y
-4x + 5y = -1

25. Objectives 3 and 4 The student will be able to:
1. graph linear functions.
2. write equations in standard form.

26. Graphing Steps
Isolate the variable (solve for y).
Make a t-table. If the domain is not given, pick your own values.
Plot the points on a graph.
Connect the points.

27. 1) Review: Solve for y 2x + y = 4
Draw “the river”
Subtract 2x from both sides
- 2x x
y = -2x + 4
2) Solve for y: x + 2y = -6
- 4x x
2y = -4x - 6
y = -2x - 3
Subtract 4x
Simplify
Divide both sides by 2

28. 3) Solve for y: x - 3y = 6 - x - x -3y = -x + 6 -3 -3 or Subtract x
Subtract x
Simplify
Divide both sides by -3 or

29. Review: Make a t-table If f(x) = 2x + 4, complete a table using the domain {-2, -1, 0, 1, 2}.
ordered pair -2
2(-2) + 4 = 0 (-2, 0)
2(-1) + 4 = 2 (-1, 2)
2(0) + 4 = 4 (0, 4)
2(1) + 4 = 6 (1, 6)
2(2) + 4 = 8 (2, 8) -1 1 2

30. Given the domain {-2, -1, 0, 1, 2}, graph 3x + y = 6
Solve for y: x + y = 6
Subtract 3x
- 3x x
y = -3x + 6
2. Make a table
ordered pair x
-3x + 6 -2 -1 1 2
-3(-2) + 6 = 12 (-2, 12)
-3(-1) + 6 = 9 (-1, 9)
-3(0) + 6 = 6 (0, 6)
-3(1) + 6 = 3 (1, 3)
-3(2) + 6 = 0 (2, 0)

31. Given the domain {-2, -1, 0, 1, 2}, graph 3x + y = 6
Plot the points (-2,12), (-1,9), (0,6), (1,3), (2,0)
Connect the points.
Bonus questions!
What is the x-intercept?
(2, 0)
What is the y-intercept?
(0, 6)
Does the line increase or decrease?
Decrease

32. Which is the graph of y = x – 4?.

33. Standard Form Ax + By = C A, B, and C have to be integers
An equation is LINEAR (the graph is a straight line) if it can be written in standard form.
This form is useful for graphing (later on…).

34. Determine whether each equation is a linear equation.
4x = 7 + 2y
Can you write this in the form
Ax + By = C?
4x - 2y = 7
A = 4, B = -2, C = 7
This is linear!

35. here

36. Determine whether each equation is a linear equation.
2) 2x2 - y = 7
Can you write it in standard form?
NO - it has an exponent!
Not linear
3) x = 12
x + 0y = 12
A = 1, B = 0, C = 12
Linear

37. Here’s the cheat sheet! An equation that is linear does NOT contain the following:
Variables in the denominator
Variables with exponents
Variables multiplied with other variables.
xy = 12

38. Is this equation linear?
Yes No
Standard Form
x – 4y = 3

39. Is this equation linear?
Yes No
Exponents are not allowed!

40. Is this equation linear? y = -3
Yes No
Standard Form
0x + y = -3

41. Bell Ringer 10/14/14 Solve for y. Evaluate the following expression
Evaluate the following expression
Domain: -4, -2, 0, 2, 4

42. Objective 4 and 5 The student will be able to:
find the x- and y-intercepts of linear equations.

43. What does it mean to INTERCEPT a pass in football?
The path of the defender crosses the path of the thrown football.
In algebra, what are x- and y-intercepts?

44. What are the x- and y-intercepts?
The x-intercept is where the graph crosses the x-axis.
The y-coordinate is always 0.
The y-intercept is where the graph crosses the y-axis.
The x-coordinate is always 0.
(2, 0)
(0, 6)

45. Find the x- and y-intercepts. 1. x - 2y = 12
x-intercept: Plug in 0 for y.
x - 2(0) = 12
x = 12; (12, 0)
y-intercept: Plug in 0 for x.
0 - 2y = 12
y = -6; (0, -6)

46. Find the x- and y-intercepts. 2. -3x + 5y = 9
x-intercept: Plug in 0 for y.
-3x - 5(0) = 9
-3x = 9
x = -3; (-3, 0)
y-intercept: Plug in 0 for x.
-3(0) + 5y = 9
5y = 9
y = ; (0, )

47. Find the x- and y-intercepts. 3. y = 7 ***Special case***
x-intercept: Plug in 0 for y.
Does 0 = 7?
No! There is no x-intercept. None
What type of lines have no x-intercept?
Horizontal!
Horizontal lines…y = 7…y-int = (0, 7)

48. What is the x-intercept of 3x – 4y = 24?
(3, 0)
(8, 0)
(0, -4)
(0, -6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

49. What is the y-intercept of -x + 2y = 8?
(-1, 0)
(-8, 0)
(0, 2)
(0, 4) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

50. What is the y-intercept of x = 3?
(3, 0)
(-3, 0)
(0, 3)
None 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

51. Objective The student will be able to:
find the slope of a line given 2 points and a graph.

52. What is the meaning of this sign?
Icy Road Ahead
Steep Road Ahead
Curvy Road Ahead
Trucks Entering Highway Ahead

53. Slope is the steepness of a line.
What does the 7% mean? 7%
7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally.
7 feet
100 feet
So, what is slope???
Slope is the steepness of a line.

54. Slope can be expressed different ways:
A line has a positive slope if it is going uphill from left to right.
A line has a negative slope if it is
going downhill from left to right.

55. 1) Determine the slope of the line.
When given the graph, it is easier to apply “rise over run”.

56. Determine the slope of the line.
Start with the lower point and count how much you rise and run to get to the other point!
rise 3 = =
run 6 6 3
Notice the slope is positive AND the line increases!

57. 2) Find the slope of the line that passes through the points (-2, -2) and (4, 1).
When given points, it is easier to use the formula!
y2 is the y coordinate of the 2nd ordered pair (y2 = 1)
y1 is the y coordinate of the 1st ordered pair (y1 = -2)

58. You can do the problems either way! Which one do you think is easiest?
Did you notice that Example #1 and Example #2 were the same problem written differently? 6 3
(-2, -2) and (4, 1)
You can do the problems either way!
Which one do you think is easiest?

59. Find the slope of the line that passes through (3, 5) and (-1, 4).-4
- ¼

60. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

61. Determine the slope of the line shown.-2 -½ 2

62. Determine the slope of the line.-1
Find points on the graph.
Use two of them and apply rise over run. 2
The line is decreasing (slope is negative).

63. What is the slope of a horizontal line?
The line doesn’t rise!
All horizontal lines have a slope of 0.

64. What is the slope of a vertical line?
The line doesn’t run!
All vertical lines have an undefined slope.

65. Draw a line through the point (2,0) that has a slope of 3.
1. Graph the ordered pair (2, 0).
2. From (2, 0), apply rise over run (write 3 as a fraction).
3. Plot a point at this location.
4. Draw a straight line through the points. 1 3

66. To solve this, plug the given information into the formula
The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.
To solve this, plug the given information into the formula

67. To solve for r, simplify and write as a proportion.
Cross multiply.
1(-4) =
4(4 – r)

68. Simplify and solve the equation. 1(-4) = 4(4 – r)
-20 = -4r
5 = r
The ordered pairs are (5, 6) and (4, 2)