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 lineCompare 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 GraphTo Review Basics Click Here 15Distance (thousand Heightfeet)(thousand feet)10Slope TABLESTABLES5 -15 -10 -5 51015-5End ShowINTERCEPTSORDERED -10 PAIRS -15 Functions 3. Click Y-axis Herehttp://ww w.printfreegr aphpaper.coFor Practice m/ to PrintActivity Graph Paper Click Here5Explaining the Basics of a Cartesian GraphClick Here (Try some of the interactive activities at this site as well!)-5 (0,0) Origin 5X-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 theyre-create your original drawing. (Dont let them see your pictureahead!) Click here to Coordinate Graph LessonClick 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 3456 78910Height 2 4 6810 1214 16 18 20 (mm)This flower is growing at a constant rate; therefore, it islinear. 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)1234Distance 25,000 40,000 55,000 70,000 (Km)Click Here to Reviewordered 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)1 234 5678 910x Height (mm) 2 468 10 12 14 1618 20Y 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) 123 4Distanc 25,000 40,000 55,00070,000e (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 ifready for tolearn Slope Plot the ordered pairs on graph paper and connect to form a line. If astraight 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 5678910Height 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 found20 15 from knowing eitherHeight 10one of these:5-10 -5 510 x -5 Day(s) a. Two ordered pairs on a -10 graph line.b. Two ordered pairs on atable.Can you determine the slope?Click on Video Lesson to learnhow. Video Lesson on Slope Click Here 18. Slope =Slope = change in Ychange in XUse 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 - 1 189 18 divided by 9Slope =2 Can you also see that you can use the rate of change in the table as the slope? Day(s) 123 4 5678910Height 246 8 10 12 14 16 18 20 (mm) 20. What is the rate of change?Hour(s)1234 Distance 25,000 40,000 55,000 70,000 (Km)Ready for InterceptsDetermine the slope of the line from two Click Hereordered pairs on the graph & compare. 21. InterceptsClick 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 whenready to learnClick 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 67 8910 x Height 2 4 6 8 1012 1416 18 20 (mm) y 25. The y-intercept is 0. The x-intercept is 0.Click Here when ready to learnaboutEquations 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 FormulaClick HereClick 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 lessonand web page lesson.) 29. The equation is: Y=2x Day(s) 1 2 3 45 678 910 x Height 2 4 6 81012 14 1618 20 (mm) yCan you also see how you could plug in the valuefor 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? TablesOrdered PairsGraphsSlopeInterceptsEquationsFunctions Go back and review any section you are not confident with yet. Review 33. The End