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- 1. Tables, Graphs, & Equations Cheryl Cresci Department of Education Math Standard 2- End Show Algebraic Reasoning. Grade 8: Determine the slope of a line given two points on the line (as coordinates, in a graph, in a table) Use y-intercept and slope to graph the equation of a line Compare the rates of change in tables and graphs and classify them as linear or nonlinear Write an equation given the tabular or graphic form of a linear problem Analyze the interrelationships among tables, graphs, and equations of lines, paying particular attention to the meaning of intercept and slope in the context of the problem
- 2. The Coordinate Graph To Review Basics Click Here 15 Distance (thousand Height feet) (thousand feet) 10 Slope TABLES TABLES 5 -15 -10 -5 5 10 15 -5 End Show INTERCEPTS ORDERED -10 PAIRS -15 Functions
- 3. Click Y-axis Herehttp://ww w.printfreegr aphpaper.co For Practice m/ to Print Activity Graph Paper Click Here 5 Explaining the Basics of a Cartesian Graph Click Here (Try some of the interactive activities at this site as well!) -5 (0,0) Origin 5 X-axis -5
- 4. Print Graph Paper http://www.print freegraphpaper.c om/ Practice making and using your own graph: Click Here 1. Make the x-axis and label with integers. 2. Make the y-axis and label with integers. 3. Label the four quadrants. 4. Make a simple drawing and list the order pairs on a separate sheet. 5. Give the list of ordered pairs to a partner and see if they re-create your original drawing. (Don’t let them see your picture ahead!) Click here to Coordinate Graph Lesson Click Here next review Tables
- 5. Distance (thousand feet) Height (thousand feet) Collected data can be entered into a table to then create ordered pairs, lines on a graph, and equations.
- 6. We could use a table to chart the height of the flowers as time passes.
- 7. Day(s) 1 2 3 4 5 6 7 8 9 10 Height 2 4 6 8 10 12 14 16 18 20 (mm) This flower is growing at a constant rate; therefore, it is linear. If it is not growing at a constant rate it is non- linear.
- 8. We can create a table showing the distance traveled with time……
- 9. Hour(s) 1 2 3 4 Distance 25,000 40,000 55,000 70,000 (Km) Click Here to Review ordered Pairs This airplane is traveling at a constant rate; therefore it is linear.
- 10. Video on Graphing Ordered Pairs Click here
- 11. This table can be listed as ordered pairs Day(s) 1 2 3 4 5 6 7 8 9 10 x Height (mm) 2 4 6 8 10 12 14 16 18 20 Y The ordered pairs would be: (x, y) (1,2) (2,4) (3,6) (4,8) (5,10) (6,12) (7,14) (8,16) (9,18) (10,20)
- 12. This table can be turned into ordered pairs: Hour(s) 1 2 3 4 Distanc 25,000 40,000 55,000 70,000 e (Km) The ordered pairs would be: (x, y) (1, 25,000) (2, 40,000) (3, 55,000) (4, 70,000)
- 13. Graphing Ordered Pairs (click for review) Use a separate graph for each. (x, y) (1,2) (x, y) (2,4) (1, 25,000) (3,6) (2, 40,000) (4,8) (3, 55,000) (5,10) (4, 70,000) (6,12) (7,14) (8,16) (9,18) (10,20) Click Here if ready for to learn Slope Plot the ordered pairs on graph paper and connect to form a line. If a straight line forms than this graph is linear.
- 14. Slope Tutorial Click Here
- 15. How much is the flower growing each day? Day(s) 1 2 3 4 5 6 7 8 9 10 Height 2 4 6 8 10 12 14 16 18 20 (mm)
- 16. The amount it is growing is 2mm per day. This is the rate of change. The rate of change is also called the slope of the line.
- 17. y Slope can be found 20 15 from knowing either Height 10 one of these: 5 -10 -5 5 10 x -5 Day(s) a. Two ordered pairs on a -10 graph line. b. Two ordered pairs on a table. Can you determine the slope? Click on Video Lesson to learn how. Video Lesson on Slope Click Here
- 18. Slope = Slope = change in Y change in X Use your knowledge gained from the video lesson on slope and Determine the slope of the line for the flower example.
- 19. (You could use any two ordered pairs and you would get the same answer for slope.) If you used the ordered pairs (1,2) and (10, 20): 20 - 2 10 - 1 18 9 18 divided by 9 Slope =2 Can you also see that you can use the rate of change in the table as the slope? Day(s) 1 2 3 4 5 6 7 8 9 10 Height 2 4 6 8 10 12 14 16 18 20 (mm)
- 20. What is the rate of change? Hour(s) 1 2 3 4 Distance 25,000 40,000 55,000 70,000 (Km) Ready for Intercepts Determine the slope of the line from two Click Here ordered pairs on the graph & compare.
- 21. Intercepts Click Here
- 22. Y-intercept …… is where the line crosses the Y-axis. X-intercept…….is where the line crosses the x-axis.
- 23. Click Here for Video on X & Y Intercepts Click Here when ready to learn Click Here for a Lesson on X & Y Intercepts about Equations (Try some of the practice problems.)
- 24. Can you determine the intercepts? Day(s) 1 2 3 4 5 6 7 8 9 10 x Height 2 4 6 8 10 12 14 16 18 20 (mm) y
- 25. The y-intercept is 0. The x-intercept is 0. Click Here when ready to learn about Equations
- 26. Y= -5x + 17 Y=2x + 4 EQUATIONS Click Here 3x + 4y =10 -9x + 3y =27
- 27. There is more than one way to find the equation of a line. Equations of a straight line. Point-Slope Formula Click Here Click Here Video Lesson on Writing Equation Given a Point and the Slope Video on Graphing an Equation Click Here
- 28. If the slope is 2 and passes through the point (2,4) What is the equation of this line? ( Use knowledge from watching video lesson and web page lesson.)
- 29. The equation is: Y=2x Day(s) 1 2 3 4 5 6 7 8 9 10 x Height 2 4 6 8 10 12 14 16 18 20 (mm) y Can you also see how you could plug in the value for x into the equation, solve, and obtain Y value?
- 30. If the slope of the line is 15, 000 and passes through the Point (2, 40,000) ….What is the equation of the line?
- 31. The equation is: Y=15,000x + 10,000
- 32. Can you see connections? Tables Ordered Pairs Graphs Slope Intercepts Equations Functions Go back and review any section you are not confident with yet…. Review
- 33. The End

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