CHAPTER 3 Graphing and Systems of Equations Lesson

CHAPTER 3 Graphing and Systems of Equations

Lesson 3. 1: Paired Data and Graphing Ordered Pairs Objectives: *Create a bar chart, scatter diagram, or line graph from a table of data. *Graph ordered pairs on a rectangular coordinate system. Martin-Gay, Developmental Mathematics 2

Vocabulary Definition A pair of numbers enclosed in parentheses and separated by a comma, such as (-2, 1), is called an ordered pair of numbers. The first number is called the x-coordinate of the ordered pair; the second number is called the y-coordinate. For the ordered pair (-2, 1), the x-coordinate is -2, and the y-coordinate is 1. Martin-Gay, Developmental Mathematics 3

The Cartesian Plane y-axis Quadrant II (-x, y) Quadrant I (x, y) x-axis origin (0, 0) Quadrant III (-x, -y) Quadrant IV (x, -y) Martin-Gay, Developmental Mathematics 4

Graphing an Ordered Pair To graph the point corresponding to a particular ordered pair (a, b), you must start at the origin and move a units to the left of right (right if a is positive, left if a is negative), then move b units up or down (up if b is positive, down if b is negative). Martin-Gay, Developmental Mathematics 5

Graphing an Ordered Pair y-axis Quadrant II Quadrant I (0, 4) (-4, 2) (-6, 0) (-3, -3) Quadrant III (5, 3) 3 units up x-axis 5 units right Note that the order of the coordinates is very important, since (-4, 2) and (2, -4) are located in different positions. (2, -4) Quadrant IV Martin-Gay, Developmental Mathematics 6

Problem Set 3. 1 (TB pp. 160 -163) y-axis Graph the following ordered pairs. (0, 5) 1. (3, 2) 3. (-3, 2) 13. (-4, -5/2) 17. (0, 5) (-3, 2) (3, 2) x-axis (-4, -5/2) Martin-Gay, Developmental Mathematics 7

Problem Set 3. 1 (TB pp. 160 -163) y-axis Give the coordinates of each numbered point in the figure. 19 19. (-4, 4) 23. (-3, 0) 25. (2, -2) 23 x-axis 27. (-5, -5) 25 27 Martin-Gay, Developmental Mathematics 8

Problem Set 3. 1 (TB pp. 160 -163) Graph the points (4, 3) and (-4, -1), and draw a straight line that passes through both of them. Then answer the following questions y-axis 29. Does the graph (2, 2) lie on the line? Yes x-axis 31. Does the graph (0, -2) lie on the line? No Martin-Gay, Developmental Mathematics 9

Problem Set 3. 1 (TB pp. 160 -163) 45. Jane takes a job at the local Marcy’s department store. Her job pays $8. 00 per hour. The graph shows how much Jane earns for working from 0 to 40 hours in a week. a. List 3 ordered pairs that lie on the line graph. (5, 40), (10, 80), (15, 120) b. How much will she earn for working 40 hours? Amount Earned ($) 350 300 250 200 160 200 150 $320 c. If her check for one week is $240, how many hours did she work? 30 hours 80 100 50 d. She works 35 hours one week, but her paycheck before deductions are subtracted out is $260. Is this correct? Explain 0 320 280 240 120 40 5 10 15 20 25 30 35 40 Hours worked No, she should receive $280 for working 35 hours. Martin-Gay, Developmental Mathematics 10

Problem Set 3. 1 (TB pp. 160 -163) Individual Practice: Homework Even Numbers Nos. 2, 4, 6… 56 Martin-Gay, Developmental Mathematics 11