Chapter2 Graphing Ordered Pairs

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 1 Suankularb Wittayalai Thonburi School Graphing Ordered Pairs Name Number M. 1/ Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 2 Suankularb Wittayalai Thonburi School Ordered pairs Ordered pairs are sets of numbers used for plotting points. They are always written inside parentheses, and are separated by a comma. Ordered pairs are usually seen together with a four-quadrant graph (also called a coordinate plane). This is a grid that looks like graph paper on which two perpendicular lines cross. The first number in the ordered pair tells you how far across from left to right to move, and the second number tells you how far up and down to move. You draw a small circle or point where the two numbers on the grid cross. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 3 Suankularb Wittayalai Thonburi School  Learning Competencies : Students will be able to 1. Use the terms generated by two numerical patterns to form ordered pairs. 2. Plot each point and join the points to form a line graph. This line graph will show the consistent relationship between the corresponding terms from the two patterns.  Warm Up Algebra is a category of math that is all about noticing patterns, and the relations between patterns, and displaying what the patterns are doing using a graph. The lesson, Generating Patterns & Identifying Relations, provided practice in making numerical sequences by applying skip-counting rules, such as add 3 or add 6. It looked at the relationship between the rules, and the resulting sequences, and realized that the sequence for the rule add 6 resulted in numbers that were twice as large as the sequence for the rule add 3. This pattern was consistent. It remained the same for all the corresponding terms in the sequences. A line graph can be used to visually show a consistent relationship, like the one between the two sequences. In order to make a line graph, you need to be able to write ordered pairs using the corresponding terms from the two numerical sequences you are comparing. Example 1 Let's look at the numerical sequences for the rules add 3 and add 6. Starting at zero and using the rule, “Add 3,” we get the sequence: 0, 3, 6, 9, 12, 15, 18, 21,….. Staring at zero and using the rule, “Add 6,” we get the sequence: 0, 6, 12, 18, 24, 30, 36, 42,…… The corresponding terms are circled below. We can use each circled pair to write an ordered pair that can be graphed. The two numbers are written inside a set of parentheses, and are separated by a comma. So these two number sequences give us the ordered pairs: (0, 0), (3, 6), (6, 12), (9, 18), (12, 24), (15, 30), (18, 36), (21,42). Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 4 Suankularb Wittayalai Thonburi School Example 2 From the table below, write the diagram and ordered pairs. Group Blackpink Got 7 BTS Wanna One EXO Red Vevet Number 4 7 7 11 9 5 (people) Diagram; Ordered Pairs; …………………………………………………………………………………………………………………… Example 3 From the ordered pairs below, write the table and diagram. Ordered Pairs; (Apple, 5), (Strawberry, 13.5), (Coconut, 7), (Orange, 9.5), (Mango, 12), (Pineapple, 17) Fruit Kg. Diagram; Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 5 Suankularb Wittayalai Thonburi School Ordered Pairs & Coordinate Plane Graphing Now that you know how to form ordered pairs from numerical sequences, it is time to learn how to use this information to make a line graph. We will be using a 4-quadrant graph to plot points and make our line graph. A 4-quadrant graph is shown below:  The first number in each ordered pair tells how far across the X line to move.  The second number in each ordered pair tells how far up or down on the Y line to move.  The point where the X and Y lines cross is marked \"0\" on the graph. It is called the \"origin,\" and is the starting point for plotting points. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 6 Suankularb Wittayalai Thonburi School Example 4 Let's trying graphing the relationship between two simple numerical sequences: \"add 1,\" and \"add 2.\" These rules give us: 0, 1, 2, 3, 4, 5, 6 0, 2, 4, 6, 8, 10, 12 We form the ordered pairs: (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12). We will start plotting points by putting our pencil on the origin point, (0, 0), where the X and Y lines cross Return to (0, 0) before plotting each point. (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12) A line can then be drawn through the points to show the constant relationship between the two numerical sequences. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 7 Suankularb Wittayalai Thonburi School Exercise 1 Ordered Pairs A) Write the ordered pair for each item. B) Write the item located at each ordered pairs. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 8 Suankularb Wittayalai Thonburi School Exercise 2 Identifying Quadrant A) Write the quadrant belongs to each animal. B) Write the animals belong to each quadrant. I – quadrant: ………………, ……………… II – quadrant: ………………, ……………… III – quadrant: ………………, ……………… IV – quadrant: ………………, ……………… Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 9 Suankularb Wittayalai Thonburi School Exercise 3 Quadrants & Axes Tick the relevant box for each ordered pair. Ordered I II III IV On x-axis On y-axis Pairs Quadrant Quadrant Quadrant Quadrant (3, 4) (-1, -5) (0, 7) (-3, 4) (-1, -6) (5, 0) (4, -5) (2, 8) (-9, 3) (1, -1) (-3, 0) (0, -8) Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 10 Suankularb Wittayalai Thonburi School Exercise 4 Plotting Points A) Plot each point on the coordinate grid. 1) T(3, 3) 2) S(1, 8) 3) H(2, 8) 4) E(6, 2) 5) R(5, 4) 6) L(7, 6) 7) M(3, 1) 8) V(9, 5) 9) P(7, 1) 10) A(4, 7) B) Draw each shape on the coordinate grid. 11) Draw at (3, 1) 12) Draw at (4, 5) 13) Draw at (1, 7) 14) Draw at (3, 5) 15) Draw at (7, 1) Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 11 Suankularb Wittayalai Thonburi School Exercise 5 Plotting Points-Line segments Plot each set of ordered pairs. Join the points and find the length of line segment. 1) (3, -1), (3, 4) 2) (-4, 1), (4, 1) Length of the line segment =………………… Length of the line segment =………………… 3) (-3, 1), (-3, 4) 4) (-1, -4), (1, -4) Length of the line segment =………………… Length of the line segment =………………… 5) How far an elephant is away from the grass? ………………………………………………………………… 6) Which is closer to the pond, giraffe or deer? ………………………………………………………………… 7) How many units does the lion move to catch the deer? ………………………………………………………………… Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 12 Suankularb Wittayalai Thonburi School Exercise 6 Plotting Points-Shapes Plot and join the points in the given order. Complete the figure by joining the end points. Identify the shape. 1) (2, 8), (3, 9), (5, 9), (6, 8), (5, 7), (3, 7) 2) (5, 5), (9, 5), (9, 1), (5, 1) Shape: ………………………………… Shape: ………………………………… 3) (2, 4), (3, 7), (7, 7), (6, 4) 4) (3, 9), (7, 5), (3, 2) Shape: ………………………………… Shape: ………………………………… 5) (2, 7), (8, 7), (8, 3), (2, 3) 6) (4, 7), (7, 7), (10, 4), (1,4) Shape: ………………………………… Shape: ………………………………… Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 13 Suankularb Wittayalai Thonburi School Exercise 7 Mystery Picture Plot and join the points in the given order. Complete the picture by joining the end points. Identify the mystery picture. (-6, 0), (-5, 2), (-3, 3), (-1, 4), (1, 4), (4, 2), (7, 4), (5, 0), (7, -4), (4, -2), (1, -4), (-1, -4), (-3, -3), (-5, -2) Mystery Picture: ……………………………… Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 14 Suankularb Wittayalai Thonburi School Exercise 8 Moving the Points Find the coordinates of each end point. End Start Direction (3, -4) 2 units up and 3 units left (1, 5) 5 units down and 3 units right (0, 4) 3 units right and 2 units down (-3, 1) 2 units left and 6 units up (2, 0) 7 units left and 4 units down 1) You are at (-5, 4). Move 2 units down and 3 units right. Where do you land? ……………………... 2) You are at (2, 3). Move 4 units left and 2 units up. Where do you land? …………………………….. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 15 Suankularb Wittayalai Thonburi School Exercise 9 Moving Around Note: Move the point either horizontally or vertically. DO NOT move diagonally. 1) Cory walks 7 units west and 8 units south. Which animal does he see? ............................................... 2) Which animal is closest to Cory? ............................................... 3) If Cory is at elephant safari and he walks 8 units up and 8 units right. Where would he land? ............................................... 4) Write the coordinates of giraffe’s location. ............................................... 5) Using the compass, tell him the route to reach the aquarium. ……………………………………………………………………………………………………………………………………… Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 16 Suankularb Wittayalai Thonburi School Equality of Ordered Pairs Equality of Ordered Pairs : Two ordered pairs are equal if and only if the corresponding first components are equal and corresponding second components are equal. Example 5 Two ordered pairs (a, b) and (c, d) are equal if a = c and b = d, i.e., (a, b) = (c, d). Find the values of x and y, if (2x - 3, y + 1) = (x + 5, 7) Solution By equality of ordered pairs, we have 2x - 3 = x + 5 and y + 1 = 7 ⇒ 2x - x = 5 + 3 ⇒ x = 8 and y = 7 - 1 ⇒ y = 6 Note: Both the elements of an ordered pair can be the same, i.e., (2, 2), (5, 5). Two ordered pairs are equal if and only if the corresponding first components are equal and second components are equal. Example 6 Ordered pairs (x, y) and (2, 7) are equal if x = 2 and y = 7. Example 7 Given (x - 3, y + 2) = (4, 5), find x and y. Solution (x - 3, y + 2) = (4, 5) ⇒ x - 3 = 4 and y + 2 = 5 Then x = 4 + 3 and y = 5 - 2 or x = 7 and y = 3 Example 8 Given (3a, 3) = (5a - 4, b + 1), find a. Solution (3a, 3) = (5a - 4, b + 1) Then, 3a = 5a - 4 and 3 = b + 1 ⇒ 5a - 3a = 4 and b = 3 - 1 ⇒ 2a = 4 and b = 2 ⇒ a = 4/2 ⇒a=2 Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 17 Suankularb Wittayalai Thonburi School Exercise 10 Equality of Ordered Pairs 1. From each of the ordered pairs, find the value of x and y. 1. (x, y) = (3, 5) 2. (2x, 3y) = (-2, 6) Solution Solution 3. (3x+2, 2y-1) = (5, 5) 4. (2x, y+1) = (3X-1, 2y) Solution Solution 5.  x , y  = (-1, -2) 6.  3x , 4y  = (X+1, 4)  2 3   2 3  Solution Solution Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 18 Suankularb Wittayalai Thonburi School 2. If (3x+2, 5) = (11, 2y-3 ) then x+y =? Solution 3. If (2x+1, 10) = (9, 3y-2 ) then xy =? Solution 4. If (7x+1, 11) = (8, 3y-1 ) then y-x = ? Solution 5. If (2x, 7) = (20, y+3 ) then x+y = ? Solution Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 19 Suankularb Wittayalai Thonburi School 4 A Line Graph Two groups of quantity relationships can be represented in different ways. Such as diagrams, tables, ordered pairs and graphs, when using a graph of the relationship between two groups of quantities, we can find the coordinates of the points on the graph. For example; Example 9 Jerry recorded the temperature in his room (in Degrees Fahrenheit) every two hours over a 12 hour period from noon to midnight. The results are shown in the line graph. 1) What was the approximate temperature in Jerry's room at 9 p.m.? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. 2) What was the difference between the highest and the lowest temperatures Jerry recorded? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 20 Suankularb Wittayalai Thonburi School Exercise 11 A Line Graph 1. The population of a town was recorded every twenty years from 1900 to 2020. The results are shown in the line graph. 1) What was the population of the town in the year 1900? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. 2) By how much did the population increase between 1920 and 1980? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. 3) Assuming that the trend in the population growth continues, which of the following is most likely to be the population of the town in the year 2020? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 21 Suankularb Wittayalai Thonburi School 2. The line graph shows how the population of parrots on an island declined over the ten year period from 2001 to 2010. Measurements were taken at the beginning of each year. 1) What was the total decline in the parrot population over that time? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. 2) Between which two years was the decline greatest? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. 3) From the information shown in the graph, how many times was the population of parrots equal to 34? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 22 Suankularb Wittayalai Thonburi School 3. The line graph shows how the record time for the 100 m sprint changed from 1964 when Bob Hayes of the US held the record to 2012 when Usain Bolt of Jamaica held the record. 1) From the graph, what was the maximum length of time for which the record remained unchanged? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. 2) Approximately what was the percentage change in the time from 1964 to 2012? ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. Instructor : Miss Kururat Phupaboon

Mathematics 2 MA21102 ‘’ Graphing ordered pairs’’ 23 Suankularb Wittayalai Thonburi School Mathematics 2 MA 21102 Instructor : Miss Kururat Phupaboon