document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785566>Question 785566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good morning,\r<BR>\n" );
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document.write( "I'm a student of San Francisco State University and I have a series of questions on the website WileyPLUS.  I'm not really a fan of it because its all computer and I dont know if I enter my answer wrong or if its my answer that is totally wrong.\r<BR>\n" );
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document.write( "Here is the example:\r<BR>\n" );
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document.write( "Write an equation for the line through (-3, 2) and (6, 1)<BR>\n" );
document.write( "Give an exact coefficients in fraction form.\r<BR>\n" );
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document.write( "y = f(x) = [a computer table that allows us to put an answer]\r<BR>\n" );
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document.write( "So, I came up with the slope (m) that is 1-2/6-(-3) = -1/9\r<BR>\n" );
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document.write( "so, now, I have y = -1/9x + b\r<BR>\n" );
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document.write( "I change into 2 = -1/9 (-3) + b<BR>\n" );
document.write( "18/9 = -1/9 (-27/9) + b<BR>\n" );
document.write( "-b = -27-162/-81<BR>\n" );
document.write( "-b = -199/-81<BR>\n" );
document.write( "-b = 199/81<BR>\n" );
document.write( "b = -199/81\r<BR>\n" );
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document.write( "So I change everything into : 2 = -1/9 (-3) + -199/81\r<BR>\n" );
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document.write( "I dont know if I am wrong or if the computer (website) is not expecting an answer this form.<BR>\n" );
document.write( "Maybe I should not use x and y as they are different at every point.<BR>\n" );
document.write( "But I tried everything already... and every time, I am wrong, the website is giving me a different exercise numbers...\r<BR>\n" );
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document.write( "Please help me!  Is my Math correct?\r<BR>\n" );
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document.write( "thank you!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477613 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=477613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> MINOR NOTE:<BR>\n" );
document.write( "If you cannot write the calculation on two lines, it should be<BR>\n" );
document.write( "m=(1-2)/(6-(-3)) = -1/9<BR>\n" );
document.write( "I can guess what you meant, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F9 ALIGN=MIDDLE  ALT=\"m=-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct.<BR>\n" );
document.write( "However, most computers and calculators will interpret what you enter literally.<BR>\n" );
document.write( "Those machines are sticklers about order of operations, and if you do not enter the parentheses, they will not guess at what you meant, like I did.<BR>\n" );
document.write( "They will just calculate<BR>\n" );
document.write( "m = 1-2/6-(-3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2%2F6-%28-3%29+=+1+-1%2F3+%2B+3+=+2%2F3+%2B+3+=+11%2F3 ALIGN=MIDDLE  ALT=\"1-2%2F6-%28-3%29+=+1+-1%2F3+%2B+3+=+2%2F3+%2B+3+=+11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You came up with the slope (m) that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%281-2%29%2F%286-%28-3%29%29+=+-1%2F9+ ALIGN=MIDDLE  ALT=\"m=%281-2%29%2F%286-%28-3%29%29+=+-1%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that reassured me that I was guessing right.<BR>\n" );
document.write( " <BR>\n" );
document.write( "WHAT YOU DID RIGHT:<BR>\n" );
document.write( "The slope is indeed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F9 ALIGN=MIDDLE  ALT=\"-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Your idea for finding the equation was not bad.<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F9 ALIGN=MIDDLE  ALT=\"m=-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the x- and y-coordinates of (-3,2) into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > would allow you to find the y-intercept (b).<BR>\n" );
document.write( "You just unnecessarily complicated the calculations<BR>\n" );
document.write( "(partly by not simplifying fractions when possible),<BR>\n" );
document.write( "and that led to cumersone calculations that led you to a silly mistake.<BR>\n" );
document.write( "It happens to the best of us.<BR>\n" );
document.write( "Here is how it should go:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%28-1%2F9%29%28-3%29%2Bb ALIGN=MIDDLE  ALT=\"2=%28-1%2F9%29%28-3%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%281%2F9%29%283%29%2Bb ALIGN=MIDDLE  ALT=\"2=%281%2F9%29%283%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > (product of two negative numbers is positive, just multiply the absolute values, ignoring the minus signs)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=1%2A3%2F9%2Bb ALIGN=MIDDLE  ALT=\"2=1%2A3%2F9%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplying fractions)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=3%2F9%2Bb ALIGN=MIDDLE  ALT=\"2=3%2F9%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=1%2F3%2Bb ALIGN=MIDDLE  ALT=\"2=1%2F3%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simplifying the fraction makes the work easier down the line)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F3=b ALIGN=MIDDLE  ALT=\"2-1%2F3=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > (now I may be forced to find a common denominator, I did not need to do that before)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F3-1%2F3=b ALIGN=MIDDLE  ALT=\"6%2F3-1%2F3=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3=b ALIGN=MIDDLE  ALT=\"5%2F3=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You should write the equation in slope-intercept form (y=mx+b) as<BR>\n" );
document.write( "y=(-1/9)x+5/3 and the computer should understand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F9%29x%2B5%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F9%29x%2B5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If it translates it and shows you that, you lknow you got it right.<BR>\n" );
document.write( "If you typed y=-1/9x+5/3, the computer may interpret <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F%28%229+x%22%29%2B5%2F3 ALIGN=MIDDLE  ALT=\"y=-1%2F%28%229+x%22%29%2B5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and I would toss a coin to figure out if you meant that or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F9%29x%2B5%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F9%29x%2B5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "An optional form of the solution would be<BR>\n" );
document.write( "y=-x/9+5/3 which can be rendered as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2F9%2B5%2F3 ALIGN=MIDDLE  ALT=\"y=-x%2F9%2B5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I would not know if that is one on the accepted answers, because computer tests are tricky.<BR>\n" );
document.write( " <BR>\n" );
document.write( "YOUR COMPLICATIONS AND MISTAKE: <BR>\n" );
document.write( "18/9 = -1/9 (-27/9) + b is true, but unnecessarily complicated<BR>\n" );
document.write( "-b = -1/9 (-27/9)-18/9 is true, but complicated further by insisting on having b on the left side.<BR>\n" );
document.write( "By then your head was spinning and you were bound to make a mistake.<BR>\n" );
document.write( "Then, multiplying -1/9 (-27/9) = 1/9 (27/9) = 1*27/(9*9) = 27/81,<BR>\n" );
document.write( "without noticing that the fraction 27/81 = 1/3 can be simplified<BR>\n" );
document.write( "would have taken you to<BR>\n" );
document.write( "-b = 27/81-18/9 --> -b = 27/81 -162/81 --> -b = (27-162)/81<BR>\n" );
document.write( "Unfortunately, you got the wrong sign on the product, and ended up with <BR>\n" );
document.write( "-b = (-27-162)/(-81) which you probably wrote as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b+=+%28-27-162%29%2F%28-81%29 ALIGN=MIDDLE  ALT=\"-b+=+%28-27-162%29%2F%28-81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on paper, but type here as<BR>\n" );
document.write( "-b = -27-162/-81 (I know what you mean, but a computer would not know).<BR>\n" );
document.write( "That yielded -b = (-199)/(-81), -b = 199/81, and b = -199/81, which is wrong.<BR>\n" );
document.write( " <BR>\n" );
document.write( "IN SUM:<BR>\n" );
document.write( "Simplify fractions whenever possible.<BR>\n" );
document.write( "Watch out for minus signs and parenteses.<BR>\n" );
document.write( "If the numbers/fractions in a class problem seem to get to complicated, you probably made a mistake somewher, and maybe there is an easier route to the solution.<BR>\n" );
document.write( " <BR>\n" );
document.write( "BONUS INFORMATION:<BR>\n" );
document.write( "If you have the slope and one point you can write the equation in point-slope form by filling the blanks in<BR>\n" );
document.write( "y - ___ = m (x - ___ ) withe the x- and y-coordinates of your point.<BR>\n" );
document.write( "If you chose point (-3,2), you would write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2%29=%28-1%2F9%29%28x-%28-3%29%29 ALIGN=MIDDLE  ALT=\"y-2%29=%28-1%2F9%29%28x-%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Form there, you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2%29=%28-1%2F9%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y-2%29=%28-1%2F9%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=%28-1%2F9%29x%2B%28-1%2F9%29%283%29 ALIGN=MIDDLE  ALT=\"y-2=%28-1%2F9%29x%2B%28-1%2F9%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=%28-1%2F9%29x-3%2F9 ALIGN=MIDDLE  ALT=\"y-2=%28-1%2F9%29x-3%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=%28-1%2F9%29x-1%2F3 ALIGN=MIDDLE  ALT=\"y-2=%28-1%2F9%29x-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simplifying the fraction)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F9%29x-1%2F3%2B2 ALIGN=MIDDLE  ALT=\"y=%28-1%2F9%29x-1%2F3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F9%29x-1%2F3%2B6%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F9%29x-1%2F3%2B6%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F9%29x%2B5%2F3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F9%29x%2B5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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