Welcome to Chapter 4!

1. Welcome to Chapter 4!

2. PSAE Practice 1. You are the new maintenance person for the local school and need to calculate how much wax will be required for the cafeteria floor based on its square footage. The cafeteria is 120 feet by 45 feet. What is the square footage you should use to figure the amount of wax needed for the cafeteria floor? a) 165 ft2 b) 100 ft2 c) 1000 ft2 d) 5400 ft2 e) 6000 ft2 2. You must set up tables for a wedding reception in the restaurant where you work. There will be 24 individuals and 40 couples attending. Each table seats 8 persons. How many tables should you set up? a) 3 b) 5 c) 10 d) 12 e) 13

3. 4.1 – CoordinatesObjective: To plot points and name points in the coordinate plane. A is formed by two real number lines that intersect at the origin. (x-axis and y-axis) An is a point in the coordinate plane represented by real numbers. The x-coordinate is the first number. The y-coordinate is the second number. Ex. (3,6) (x, y)  (right or left, up or down)

4. Think of coordinate points as an… (x, y)  You must move (horizontally) into the elevator before you can go up or down.

5. Coordinate plane (x, y) y-axis Quadrant II (-, +) Quadrant I (+, +) Origin (0,0) x- axis Quadrant III (-, -) Quadrant IV (+, -)

6. Plotting points To plot a point: (3,4) Start at (0,0) Move 3 to the right (positive) Then 4 up (positive) make a point • Plot these points: • (-2, -4) • (0, 3) • (-1,0) • (6,-2) • (-4, 5)

7. Practice Name the following points and give the quadrant or axis where they lie. A: B: C: D: A D C B

8. Naming Points Identify the ordered pairs on the coordinate plane. Name the quadrant it is in or the axis it is on. A________Quad _____ B ________Quad _____ C  ________ Quad _____ D  ________ Quad _____ E D B E _________ Quad _____ F  ________ Quad _____ F A C

9. The Coordinate Plane Steps to Make a Scatter Plot: • Determine what will be x and y. • x – is in charge, it changes automatically • y – depends on x, is not automatic • Determine units of each axis and label. • Find range of variable • Divide range by number of squares • Always round up to “nice” unit • Plot points.

10. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Make a Scatter Plot Example The age (in years) of seven used cars and the price (in thousands of dollars) paid for the cars are recorded in the table. Make a scatter plot and explain what it indicates. price in $1,000 age of car How much would a 2-year old car cost?

11. Make a Scatter Plot Example The amount (in millions of dollars) spend in the United States on snowmobiles is shown in the table. Make a scatter plot and explain what it indicates.

12. Lesson 4.1 DHQ • NONE TODAY Tonight’s Homework Assignment: Coordinate WORKSHEET

13. Warm-Up • Solve each equation for y. • 2x + y = 10 2) 6x – 3y = -3 • Find the value of y when x = -3. • y = x – 7 4) y = -5x + 1

14. 4.2 – Graphing Linear Equations • OBJECTIVES • Graph a using a table. • Graph and lines. linear equation horizontal vertical Note (1) All the Equations in Chap 4 refer 2 variable Linear Equations. (2) The graph of each linear equation is a LINE.

15. Solution of an Equation It is an ordered pair (x, y) that makes an equation true. Example: x + 3y = 6 • Is (-3, 3) a solution?

16. Is (-3, 3) the only solution? • x + 3y = 6 • In pairs, try to come up with other solutions to the equation! • Try to come up with at least 2 more solutions.

17. Solutions of the Equation x + 3y = 6 Solutions: What would it look like if we plotted the solutions of the equation on a coordinate plane?

18. Solutions to a Linear Equation • All the that lie on the line are the solutions to the ! points equation How many solutions did we have in our previous example?

19. How to Check if a Point is a solution • Method 1: Using a Graph • Check to see if the point is on the line. Is (3, 1) a solution of the equation 2x – y = 5? Is (0, -4) a solution of the equation 2x – y = 5? Is (5, 5) a solution of the equation 2x – y = 5?

20. How to Check if a Point is a solution Method 2: Checking algebraically • Plug the point into the equation and see if it is true. Is (3, 1) a solution of the equation 2x – y = 5? Is (0, -4) a solution of the equation 2x – y = 5? Is (5, 5) a solution of the equation 2x – y = 5?

21. Break Time Use this time to relax, stretch out, talk to a neighbor, or try the following rebus puzzles.

22. Using a table to graph an equation • Steps: • Rewrite the equation so that it says “y = …” – (called function form) • Make a table and choose values for x. • Plot the points on a coordinate plane and graph with a straight line.

23. Use a table to graph the following equation y + 1 = 2x Step 1: Rewrite the equation so that it says “y = …” Step 2: Make a table and choose values for x.

24. Use a table to graph the following equation y + 1 = 2x Step 3: Plot the points on a coordinate plane and graph with a straight line.

25. Pairs Practice Graph y + 2 = 3x.

26. Pairs Practice Graph y + 3 = x.

27. Graphing Horizontal and Vertical Lines • Horizontal = left to right • Vertical = up and down MEMORIZE THIS! x = any number vertical line horizontal line y = any number

28. Horizontal Lines

29. Graph the following Equation y = 5 Horizontal line where every y-coordinate on the line is 5.

30. Graph the following Equation y = -1

31. Vertical Lines

32. Graph the following Equation x = -3 Vertical line where every x-coordinate on the line is -3.

33. Graph the following Equation x = 5

34. Lesson 4.2 DHQ • Decide whether the given ordered pair is a solution of 2x – 3y = 8. • (-2, -4) b. (7, -2) • Rewrite 4x – 2y = 18 in function form. • Tonight’s Homework Assignment: • Page/s: 214-215 • #’s 15-20, 30-32, 36-37, 60

35. 4.3 - Quick Graphs Using Intercepts Objectives: • Find the intercepts of a graph of a linear equation.

36. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6

37. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6

38. How many points does it take to determine a line? We need at least twopoints to determine a line.

39. Intercepts x-intercept– the point where a line or curve crosses the x-axis. This is always written as (x, 0). y-intercept– the point where a line or curve crosses the y-axis. This is always written as (0, y).

40. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6 Intercepts y-intercept? (0, 3) y = 3 x-intercept? (2, 0) x = 2

41. What if we are not given a graph? How do we determine the x and y-intercepts?

42. We can find the… • x-intercept by setting y = 0 • y-intercept by setting x = 0

43. Find the x-intercept and y-intercept of the graph of the following equation. • To find the x-intercept, set y = 0 and solve for x. • To find the y-intercept, set x = 0 and solve for y. 2x + 3y = 6

44. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6 Find the x-intercept and y-intercept. Then graph the line. 2x – y = 4

45. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6 Find the x-intercept and y-intercept. Then graph the line. y – 2x = 3

46. Break Time • Use this time to relax, stretch out, talk to a neighbor, or try the following rebus puzzles.

47. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6 Find the x-intercept and y-intercept. Then graph the line. y = 2x + 4

48. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6 Graph and write the equation of the horizontal line passing through (3, -4) and (-6, -4).

49. 7 6 5 4 3 2 1 -6 -4 -2 1 2 3 4 5 6 7 -2 -4 -6 Graph and write the equation of the vertical line passing through (3, 2) and (3, -5).

50. Recap: • The x-intercept and y-intercept are the points at which a line or curve cross the x and y-axis, respectively. • To find the x-intercept, set y = 0. • To find the y-intercept, set x = 0. • We can graph a line by connecting the two intercepts.