Question 23743: My algebra teacher is rapidly trying to teach us Direct Variation(ax+b=0), she says it's similar to (y=mx+b) but she's not telling me and my classmates how?
So could you help me understand how to work direct variation...
here's one of the problems we had in class...
2x-5=1
she tells us to graphicaally, then check it algebraically, but I don't even understand how to start.
Would you please help me?!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE MY COMMENTS BELOW
My algebra teacher is rapidly trying to teach us Direct Variation(ax+b=0),
DONT WORRY WE WILL HELP YOU..OK.
MAY BE TEACHER HAS GOT SOME COMPULSION TO FINISH THE COURSE WORK.
she says it's similar to (y=mx+b) but she's not telling me and my classmates how?..SIMILAR IS NOT VERY TRUE ...IT IS PARTIALLY APPLICABLE..I SHALL SHOW YOU BY EXAMPLES BELOW..ANY WAY NO POINT IN CONTRADICTING YOUR TEACHER.FIRST TRY TO UNDERSTAND..IT IS PRETTY SIMPLE..
So could you help me understand how to work direct variation...
OK LET US GO WITH SOME EXAMPLES ON DIRECT VARIATION..SUPPOSE YOU ARE GIVING CHACOLATES TO YOUR CLASS MATES ON YOUR BIRTH DAY...YOU ARE GIVING 1 CHACOLATE PER STUDENT SAY..SO IF THERE ARE 10 STUDENTS YOU NEED 10 CHACOLATES..IF THERE ARE 20 STUDENTS YOU NEED 20 CHACOLATES.SUCH A PROPERTY IS CALLED DIRECT PROPORTION.WE SAY NUMBER OF CHACOLATES REQUIRED VARIES DIRECTLY OR IS IN DIRECT PROPORTION TO NUMBER OF STUDENTS.IF WE DESIGNATE NUMBER OF STUDENTS BY S AND NUMBER OF CHACOLATES REQUIRED BY C..THEN WE SAY
C IS DIRECTLY PROPORTIONAL TO S..
YOU WILL FIND IN THE CASE OF DIRECT PROPORTION , C/S IS ALWAYS CONSTANT..SO WE SAY MATHEMATICALLY C=K*S...OR...C/S=K......WHERE K IS A CONSTANT...IN THIS CASE WE FIND 10/10=20/20=...ETC...=1 CONSTANT ALWAYS..THIS IS THE CHARACTERSTIC PROPERTY OF DIRECT PROPORTION OR VARIATION .HOPE IT IS CLEAR NOW..YOU CAN THINK OF OTHER EXAMPLES ...
NOW WHY I SAID Y=M*X+B IS NOT STRICTLY CORRECT YOU CAN SEE ...Y=M*X IS DIRECT PROPORTION (WE CALLED IT C=K*S...C IN PLACE OF Y , S IN PLACE OF X AND K IN PLACE OF M )BUT B IS NOT ALLOWED IN DIRECT PROPO RTION AS THEN YOU CAN SEE THAT Y/X WILL NOT BE CONSTANT..SAY Y=X+1...THEN WE HAVE WHEN X=10..Y=10+1=11 AND WHEN X=20 ,WE HAVE Y=20+1=21 AND Y/X IS 11/10 IN ONE CASE AND 21/20 IN ANOTHER CASE..THEY ARE NOT EQUAL AND HENCE Y/X IS NOT CONSTANT AND HENCE WE CANNOT SAY THAT Y AND X ARE IN DIRECT PROPORTION...HAD IT BEEN ONLY Y=M*X ,IT IS CORRECT ,BUT NOT Y=M*X+B.
here's one of the problems we had in class...
2x-5=1...I THINK IT SHOULD BE 2X-1=Y..TO GRAPH THIS GIVE DIFFERENT VALUES TO X ,FIND Y FROM THE EQUATION ...
ALGEBRAICALLY....AT X=0 , Y= 2*0-5=0-5=-5....ETC...
AND TABULATE AND PLOT AS SHOWN BELOW.
X...............0....1.........2......3........4........5.....ETC..
Y=2X-5.........-5...-3........-1.....1........3........5...ETC...
THAT IS THE GRAPHIC REPRESENTATION ..IT IS A STRAIGHLINE WITH A SLOPE OR GRADIENT OF 2 (SIMILAR TO OUR CONSTANT K...BUT FOR THAT B TERM OF -5).
NOW IF WE HAVE TO HONOUR YOUR TEACHERS SAYING WE HAVE TO DISCOUNT THAT B EVERY TIME OR TAKE IT AS A BASIS OR DATUM OR BOTTOM POINT OVER WHICH WE MEASURE X. IF WE DISCOUNT THAT B ,THAT IS TAKE DIFFERENCE IN Y VALUE AND DIFFERENCE IN X VALUE ,THEN THEY ARE IN DIRECT PROPORTION .YOU CAN SEE FROM THE ABOVE
DIFFERENCE IN X .....1-0=1...............2-1=1......ETC
DIFFERENCE IN Y .....-3-(-5)=2...........-1-(-3)=2.......ETC
RATIO................2/1=2..................2/1=2..............ETC....
she tells us to graphicaally, then check it algebraically, but I don't even understand how to start.
Would you please help me?!...HOPE THIS WOULD HAVE HELPED YOU TO UNDERSTAND A LITTLE BETTER...
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