University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

358

Pages:

1
Author:

Maverick Haynes

Mini-Lecture 3.1 Reading Graphs and the Rectangular Coordinate System Learning Objectives: 1. Read bar and line graphs. 2. Define the rectangular coordinate system and plot ordered pairs of numbers. 3. Graph paired data to create a scatter diagram. 4. Determine whether an ordered pair is a solution of an equation in two variables. 5. Find the missing coordinate of an ordered pair solution, given one coordinate of the pair. Examples: 1. a) The following bar graph shows points scored per quarter in a basketball game. Use the bar graph to find the final score. b) The following line graph shows the average monthly rent for people in Worcester. How much did monthly rent increase from 1980 – 2000. 35 Points per Quarter 25 20 Celtics 15 Lakers 10 5 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Rent in $ per Month 30 1600 1400 1200 1000 800 600 400 200 0 1980 1990 2000 2. Plot each order pair. State in which quadrant or on which axis each point lies. ⎛ 2 1⎞ a) (-2, -5) b) (0, -4) c) ⎜ 2 , 4 ⎟ d) (-1, 4) ⎝ 3 2⎠ 3. The table gives a bookstore’s net dollar sales for the period of 2000-2005. Year 2000 2001 2002 2003 2004 2005 (x) Sales – in thousands 19 22 21 23 25 26 (y) a. Write this paired data as a set of ordered pairs of the form (year, sales) b. In your own words, write the meaning of the order pair. c. Create a scatter diagram of the paired data. 4. Determine whether each ordered pair is a solution of the given linear equation. 1 a) 5x + y = 15; (1,4), (2,5), (0, 15) b) x = y ; (1,4), (8,2), (0,0) 4 5. Complete each ordered pair so that it is a solution of the given linear equation. 1 1⎞ ⎛ a) x + 2 y = 6 ; (2, ), ( , -3) b) y = x − 2; ( 6, ) , ⎜ , − ⎟ 3 3⎠ ⎝ Teaching Notes: • Most students can read bar and line graphs successfully. • Many students have trouble putting meaning to an ordered pair. • Remind students that an ordered pair is (x, y) – alphabetical order. • Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 88 to 82; 1b) $1000; 2a) III; 2b) y-axis; 2c) I; 2d) II; 3a) { (2000,19), (2001,22), (2002, 21), (2003, 23), (2004, 25), (2005, 26)}; 3b) answers will vary; 4a) No, Yes, Yes; 4b) Yes, No, Yes; 5a) (2, 2), (12, -3); 5b) (6, 0), (5, − 1 ) 3