1. Unit 2 Lesson 1: The Coordinate Plane Objectives: To plot points on a coordinate plane To name points on a coordinate plane

2. Y-axis X-Axis Quadrant IQuadrant II Quadrant IIIQuadrant IV When you have a horizontal and vertical number line set up as the one pictured, this is called a coordinate plane. Origin

3. Naming a point on a plane: (x,y) Coordinates are an ordered pair of numbers that locates a point in the coordinate plane. 2 3 The coordinates of this point is (2,3)

4. Example 1: What are the coordinates of the following points? A: B: C: D: (4,4) 4 4 -3 (-3,-3) (3,-6) (-5,2)

5. Example 2: Graph each of the following points on the coordinate plane. A: (-5,1) B: (6,5) C: (-5,0) D: (0,0) E: (-1, -4)

6. Now let’s try it in our classroom’s coordinate plane!

7. Example 3: Make a table for the equation y=2x X-20123 y -4-20246 Now, plot these points on a coordinate plane!

8. X-20123 F(x) Example 4: Make a table for the equation f(x) = -5x +4 1494-6-11 *If your numbers do not fit, you may have to change your scale!*

9. Describing Graphs Objectives: To be able to label and describe an event based on a graph To be able to sketch a graph based on a description of an event

10. Commute: One student walks and takes a bus to get from school to home each day. The graph below, shows the student’s commute by relating the time the student spends commuting and the distance he travels. Describe what the graph shows by labeling each part.

11. Independent Variable vs. Dependent Variable Example: From the Commuter graph Dependent variable: the variable whose value depends on the value of the other variable *This value is always represented on the y-axis Independent variable: the variable whose value does not depend on the value of the other variable *This value is always represented on the x-axis Dependent Variable: Distance Independent Variable: Time Depends on

12. Example 2: Label each section of the graph.

13. Sketching a graph: Travel: A plane is flying from New York to London. Sketch a graph of the plane’s altitude during the flight (the flight includes taking off, cruising altitude, circling the runway, and landing). Label each section.

15. Your friend said that this graph describes a person bicycling up and then down a hill. Explain your friend’s error.

16. Objectives: To determine the domain and range of a relation To describe a graph as increasing, decreasing, or constant

18. Domain and Range of a Relation A relation is a set of ordered pairs (coordinates). The (age, height) ordered pairs below form a relation

19. Domain of a relation: the first coordinates (x or input) in a set of ordered pairs of a relation Domain: {,,,} 14182021 Range: {,,,, } 4.254.404.855.005.25 *Notice we only write 18 once in our domain Range of a relation: the second coordinates (y or output) in a set of ordered pairs of a relation or function

20. Example 2: START OF GUIDED NOTES Find the Domain and Range for the ordered pairs below. a ) (2,3), (3,4), (6,7), (4,10) Domain: {2,3,4,6} Range: {3,4,7,10} b)(3,15), (7,-35), (-1,5), (4,15) Domain: {-1,3,4,7} Range: {-35,5,15}

21. 100200300400500600 152025303540 Example 2: State the domain and range. a) Domain:Range:

22. 10.511.512.513.514.515.5 403020100-10 Example 3: State the domain and range. Domain:Range:

23. Example 3: a)Find the Domain and Range for the graphs below. b)Describe the intervals as increasing, decreasing, or constant c)Identify the independent and dependent variable a)Domain:Range: b) fromto c) Is the dependent variable. is the independent variable.

24. Domain:Range: Description:

25. Domain: Range: Description:

26. Domain: Range: WARM UP:

27. WARM UP: State if the following graph is a function. Then give its domain and range. Function (yes/no): Domain: Range: Description:

29. A function is a relation that assigns exactly one output (range) value for each input (domain) value. Example: Y = 3x + 4 OutputInput X (input)Y (output) 1 2 3 4 7 10 13 16

30. Vertical-Line test: If any vertical line passes through more than one point of the graph, then the relation is not a function. How do we tell if a relation is a function?

31. Example 1: Determine whether the relation is a function. a) { (5,-2), (9,-1), (-4,-2), (7,7) }

32. Example 2: Determine whether the relation is a function using a mapping diagram. a) { (-2,-1), (-1,0), (6,3), (-2,1) } TRY ONE:

33. Does this graph represent a functio n ?

35. State if the following graph is a function. Then give its domain and range. Function: Domain: Range: TRY ONE:

36. Example 2: TRY ONE: Make a table for f(x) = -2x -4 X-2x -4F(x) 0 1 2 3 Domain: Range: Function (yes/no): Graph the points from our table and connect them to form a line.

38. Reasonable Domain and Range: Miranda earns $7 per hour for babysitting after school and on Saturday. She works no more than 16 hours per week. a)Identify the independent and dependent quantities. b)Find the reasonable domain and range c)Write the reasonable domain and range as inequalities

39. Alexis downloads songs for $.75 each. He has between $3.00 and $6.00 to spend on songs. a)Identify the independent and dependent quantities for this situation b) Find the reasonable domain and range values. c) Write the domain and range as inequalities. TRY ONE:

40. Your turn to practice! We will go over numbers 1-3 in 5 minutes!

41. Exit Slip: State the domain and range of the graph and whether it is a function.

42. RATE OF CHANGE Change in y Change in x

43. Hours12345 Babysitting Cost 2535455565 Rate of Change:

44. Minutes2030405060 Miles246810 Rate of Change:

45. Miles100200300400500 Rental Cost 4550556065 Rate of Change: TRY ONE:

46. What do you think of when you hear the word slope?

48. Example 2: Find the rate of change and slope from a graph Rate of Change: Slope: Rise 3 Run 2

49. Rate of Change: Slope: TRY ONE:

50. Rate of Change: Slope:

51. Rate of Change: Slope: TRY ONE:

52. Rate of Change: Slope: TRY ONE:

53. Rate of Change: Slope:

54. Can we find slope some other way? Why, yes! You can! Rate of change: change in y change in x Slope (m): y 2 -y 1 x 2 -x 1

55. Example: Find the slope of the line containing the points (4,5) and (6,1) using the slope formula Step 1: Write the slope formula M = y 2 -y 1 x 2 -x 1 Step 2: Label your coordinates (4,5)(6,1) x1x1 x2x2 y1y1 y2y2 Step 3: Substitute your values into the formula M = 1-5 6-4 Step 4: Calculate your slope M = 1-5 6-4 M = -4 2 M = -2

56. Example: Find the slope of the line containing the points (-2,4) and (-4,-2) using the slope formula TRY ONE: Step 1: Write the slope formula M = y 2 -y 1 x 2 -x 1 Step 2: Label your coordinates(, ) Step 3: Substitute your values into the formula M = Step 4: Calculate your slope M =

59. Here is an equation in standard form, if y = 0 solve for x Here is an equation in standard form, if x = 0 solve for y Don’t say standard form Okay now if y = 0 what is x? how do we write this as an ordered pair? Okay now if x = 0 what is y? How do we write this as an ordered pair? Okay now lets graph these points Okay now lets connect these points What do you notice about the ordered pair where y = 0? (it’s on the x axis) What do you notice about the ordered pair where x = 0? (it’s on the y axis) These are points have names, they are called intercepts. The one on the x axis is the X-intercept The one on the y axis is the Y-intercept Then have practice problems..equation, graph line using the intercepts Then move into y=mx + b (m is the slope, b is the y intercept) JUST GRAPHING Then move to writing equations given: slope and y int, two points, word problems Then graphing given an equation, slope and y int, two points, word problems Parallel and perpendicular lines..and I’m done…