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Students should recall that slope is calculated by picking any two points on the line (x1 , y1) and (x2, y2). Divide the rise (difference between the y-coordinates) by the run (difference between the x-coordinates). Slope = y2 - y1 = rise x2 – x1 run Students should also recall that a positive slope rises from left to right, a negative slope falls from left to right, a slope of zero is a horizontal line, and a vertical line has an undefined slope. Complete the table and then graph the line for the equation y = x – 4. xx - 4y (x,y)Choose a value for xSubstitute the value of xFind the value of yCreate an ordered pair Figure 1 Complete the table and draw the graph of the equation y = -x – 3.. x - x – 3y f(x) (x,y) 3. Construct and complete a table, then graph the equation of y = 7 – 2x. EMBED Word.Picture.8 Using a graphing calculator, graph the equation y = 1/2x + 1. Use the window (xmin = -10, xmax = 10, xscl = 1, ymin = -10, ymax = 10, yscl -= 1, xres = 1). Enter the equation into y= (upper left corner) and then graph (upper right corner). Sketch your findings below. What are the slopes for problems 1, 2, 3, 4? What correlation do you see between these slopes and their respective equations? Are the slopes for problems 1, 2, 3, 4 positive or negative? What correlation do you see between the signs of the slopes and their respective equations? What are the y-intercepts for problems 1, 2, 3, 4? What correlation do you see between their y-intercepts and their respective equations? Graph the equations y = 2x, y = 2x + 1, y = 2x + 2, y = 2x + 10, and y = 2x – 3. 9. What do you notice about the change in the graphs in relation to their respective equations? Graph the equations y = x + 3, y = 2x + 3, y = 3x + 3, y = 10x + 3, and Y = -2x + 3. What can you conclude about the relationship between the graphs and their respective equations? Given this graph, what is its slope? What is its y-intercept? Given this graph, what is its slope? What is its y-intercept? Given this graph, what is its slope? What is its y-intercept? Given this graph, what is its slope? What is its y-intercept? What are the equations for problems 11, 12, 13, 14? How do you know these equations correctly match their graphs? Scatter plots show the relationship between two sets of data. The two sets of data are graphed as ordered pairs on a coordinate system. When real-life data are collected, the points graphed usually do not form a straight line, but may approximate a linear relationship. Scatter plots can be used to spot trends, draw conclusions, and make predictions about the data. The relationships between the two sets of data can show a positive relationship where y increases as x increases. The plots can show a negative relationship where y decreases as x increases. There can also be no relationship if that data reveals no obvious relationship. A best-fit line is used with a scatter plot to approximate a linear relationship. A best-fit line is a line that is very close to most of the data points. Use the table to make a scatter plot and draw a best-fit line. Use the best-fit line to predict the average hourly wage of construction workers in 2010. YearAverage Hourly Earnings ($)19809.94198512.32199013.77199515.09200017.13 Use the table to make a scatter plot and draw a best-fit line. Then write an equation for the best-fit line and use it to predict the number of persons employed in mining in 2010. YearEmployees (thousands)198010271985927199070919955812000535 b 19. What concepts have you learned? Project AMP Dr. Antonio R. 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Quesada, Director ProjeC,22,'H^CN,H='2< 2HN=2.898M ,2,'2,C,222 ژˆىبct AMP ,'H^C 2 ژüىب ¸=بى'ےےûœےگ@Times New Roman- 2 ƒîىب ¸-بى'ےےœے)ج 2 ƒجج)ےœ1¸2 2 ƒ‏ج)ےœ ¸-œے)ج'ےے'ےےû{ےگ@BComic Sans MS- "2 ê)ىبSlope of a Line\$FGI(FD(D)I%FI 2 êأىب ¸]ûœےگ@BComic Sans MS- 2 €ِ ىب ¸E#2 mىبElaine Alexander>347J7;34;71 2 ىب ¸E2 —¸ ىبMinnie HarrisX447M3111 2 —4ىب ¸D2 "سىبLinda Singer74;3E4571 2 "ىب ¸E 2 îىب ¸E 2 9îىبG¸D2 92ىبoal: P532 9ٌىبYou @54s2 9¸Eىبshould be able to complete a table, graph a line, write an equation, 0:54;;72;7/535N57/73/3;74135:347D1/7347443/54s2 ؤîEىبanalyze a graph, and recognize vital parts of the equation 34346735135:34;073554671/3531/143/:77443/54 2 ؤ¤ىب ¸E2 Oîىبy = mx + b.43N;0; 2 Oعىب ¸E 2 غîىب ¸E;2 fî ىبStudents should recall that slopE/4;74/11:54;1733/:3/155O2 fآ-ىبe is calculated by picking any two points on 713334307;;453745344/E5554/154-2 ٌîىبthe line (x/:747%;û½ےگ@BComic Sans MS-2 ‏جىب1 -2 ٌ‏ىب, y4- 2 ‏lىب1¸-2 ٌٹىب) and (x%34;%:- 2 ‏ىىب2¸)-2 ٌىب, y4- 2 ‏ƒىب2¸)-O2 ٌ¬-ىب). 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slope.34;3171/3347:313444;7347;1557 2 L v ىب ¸E 2 ط îىب ¸Eûœےگ@"Arial--2 c„ىب1.-- 2 cتىب ¸P-;2 c ىبComplete the table and then grap<5N57/7/:7/3;735;/:745135>2 c0 "ىبh the line for the equation y = x :/:747341/:77443/5443: 2 cىب–¸,2 cDىب 4.= 2 c¸ىب ¸Eبى'ےے 2 î„ىب ¸E- 2 ‹„Yببx¸(- 2 ‹¬Yبب ¸(-2 ‹÷جD بx (- 2 ‹3جD ب-¸-2 ‹NجD ب 4)- 2 ‹‹جD ب ¸)-2 ‹s H ³ بy #- 2 ‹و H ³ ب ¸(-2 ‹â · )ب (x,y)'"- 2 ‹„· )ب ¸(ü- @ !ًU- - @ !ًU- - @ !ًoY- - @ !ًب- - @ !ًxج- - @ !ًD - - @ !ًkH - - @ !ً³ - - @ !ًr· - - @ !ً)- - @ !ً)- - @ !ً‹U- - @ !ً‹ب- - @ !ً‹D - - @ !ً‹³ - - @ !ً‹)- -)2 „YببChoose a value for x('##!%"!"#%"# (- 2 ùYبب ¸(-12 ÷جD بSubstitute the value of x.#( #% &%!""%#"(- 2 جD ب ¸(-(2 s H ³ بFind the value of yx)#''%!"#$#"#- 2 ·H ³ ب ¸(-,2 â · )بCreate an ordered pair( %" %"## &% %'$" - 2 ھ· )ب ¸(- @ !ً›U- - @ !ًo›Y- - @ !ً›ب- - @ !ًx›ج- - @ !ً›D - - @ !ًk›H - - @ !ً›³ - - @ !ًr›· - - @ !ً›)- - @ !ًŒںU- - @ !ًŒںب- - @ !ًŒںD - - @ !ًŒں³ - - @ !ًŒں)- - 2 ھ„Yبب ¸)- 2 ھ÷جD ب ¸)- 2 ھs H ³ ب ¸)- 2 ھâ · )ب ¸)- @ !ً+U- - @ !ًo+Y- - @ !ً+ب- - @ !ًx+ج- - @ !ً+D - - @ !ًk+H - - @ !ً+³ - - @ !ًr+· - - @ !ً+)- - @ !ً‹/U- - @ !ً‹/ب- - @ !ً‹/D - - @ !ً‹/³ - - @ !ً‹/)- - 2 9„Yبب ¸)- 2 9÷جD ب ¸)- 2 9s H ³ ب ¸)- 2 9â · )ب ¸)- @ !ً؛U- - @ !ًo؛Y- - @ !ً؛ب- - @ !ًx؛ج- - @ !ً؛D - - @ !ًk؛H - - @ !ً؛³ - - @ !ًr؛· - - @ !ً؛)- - @ !ًŒ¾U- - @ !ًŒ¾ب- - @ !ًŒ¾D - - @ !ًŒ¾³ - - @ !ًŒ¾)- - 2 ة„Yبب ¸)- 2 ة÷جD ب ¸)- 2 ةs H ³ ب ¸)- 2 ةâ · )ب ¸)- @ !ًJU- - @ !ًoJY- - @ !ًJب- - @ !ًxJج- - @ !ًJD - - @ !ًkJH - - @ !ًJ³ - - @ !ًrJ· - - @ !ًJ)- - @ !ً‹NU- - @ !ً‹Nب- - @ !ً‹ND - - @ !ً‹N³ - - @ !ً‹N)- - 2 X„Yبب ¸)- 2 X÷جD ب ¸)- 2 Xs H ³ ب ¸)- 2 Xâ · )ب ¸)- @ !ًظU- - @ !ًoظY- - @ !ًظب- - @ !ًxظج- - @ !ًظD - - @ !ًkظH - - @ !ًظ³ - - @ !ًrظ· - - @ !ًظ)- - @ !ًŒفU- - @ !ًiU- - @ !ًiU- - @ !ًoiY- - @ !ًŒفب- - @ !ًiب- - @ !ًxiج- - @ !ًŒفD - - @ !ًiD - - @ !ًkiH - - @ !ًŒف³ - - @ !ًi³ - - @ !ًri· - - @ !ًŒف)- - @ !ًi)- - @ !ًi)- - 2 è„ىب ¸.-ً ببىىااëëئئêêإإééؤؤèèأأççآآووءءههہہنن ؟ ؟م م ¾ ¾â â ½½لل¼¼àà » »ك ك 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