document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=490225>Question 490225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this Algebra problem. Thank you.\r<BR>\n" );
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document.write( "To convert the celsius tempture C to the fahenheit tempture F\r<BR>\n" );
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document.write( "x+10y=2, for y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333944 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the celsius temperature shows the freezing point at 0 degrees and the boiling point at 100 degrees.\r<BR>\n" );
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document.write( "the fahrenheit temperature shows the freezing point at 32 degrees and the boiling point at 212 degrees.\r<BR>\n" );
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document.write( "at the freezing point, the fahrenheit temperature is equal to the celsius temperature + 32 degrees.\r<BR>\n" );
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document.write( "if we let x equal to celsius temperature and we let y equal the fahrenheit temperature, and we assume a linear equation is suffiicient to model the relationship, then our formula will be:\r<BR>\n" );
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document.write( "y = mx + 32\r<BR>\n" );
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document.write( "y is the fahrenheit temperature and x is the celsius temperature.\r<BR>\n" );
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document.write( "when x is equal to 0, y is equal to 32 degrees.\r<BR>\n" );
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document.write( "that's the fahrenheit temperature when the celsius temperature is 0 degrees.\r<BR>\n" );
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document.write( "when x = 100, we know that y is equal to 212 degrees.\r<BR>\n" );
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document.write( "y = mx + b is the slope intercept form of a straight line.<BR>\n" );
document.write( "m is the slope.<BR>\n" );
document.write( "b is the y intercept.\r<BR>\n" );
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document.write( "we already found b = 32 because we know that when x is equal to 0, y is equal to 32.\r<BR>\n" );
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document.write( "that led to y = mx + 32\r<BR>\n" );
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document.write( "we now need to find m (the slope).\r<BR>\n" );
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document.write( "the slope is determined by the following equation:\r<BR>\n" );
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document.write( "m = slope = (y2-y1) / (x2 - x1)\r<BR>\n" );
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document.write( "(x1,y1) is one point on the line of the equation.<BR>\n" );
document.write( "(x2,y2) is the other point on the line of the equation.\r<BR>\n" );
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document.write( "our first point is equal to (x1,y1) which is equal to (0,32).<BR>\n" );
document.write( "that's the point where celsius (x) is equal to 0 and fahrenheit (y) is equal to 32 degrees.\r<BR>\n" );
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document.write( "our second point is equal to (x2,y2) which is equal to (100,212).<BR>\n" );
document.write( "that's the point where celsius (x) is equal to 100 and fahrenheit (y) is equal to 212 degrees.\r<BR>\n" );
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document.write( "the slope is therefore equal to (y2 - y1) / (x2 - x1) which is equal to (212 - 32) / (100 - 0) which is equal to 180 / 100 which is equal to 18 / 10 which is equal to 9 / 5.\r<BR>\n" );
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document.write( "our slope is equal to 9/5.<BR>\n" );
document.write( "our y intercept is equal to 32.\r<BR>\n" );
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document.write( "out equation is y = 9/5 * x + 32.\r<BR>\n" );
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document.write( "if you know the celsius temperature, then use this formula to find the equivalent fahrenheit formula.\r<BR>\n" );
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document.write( "if you know the the fahrenheit temperature, then the formula to find the celsius temperature is derived from this formula as follows:\r<BR>\n" );
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document.write( "start with y = 9/5 * x + 32<BR>\n" );
document.write( "subtract 32 from both sides of this equation to get:<BR>\n" );
document.write( "y - 32 = 9/5 * x<BR>\n" );
document.write( "multiply both sides of this equation by (5/9) to get:<BR>\n" );
document.write( "5/9 * (y - 32) = x<BR>\n" );
document.write( "this is the equation to convert from fahrenheit to celsius.\r<BR>\n" );
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document.write( "to convert from celsius to fahrenheit, the equation is:<BR>\n" );
document.write( "y = 9/5 * x + 32<BR>\n" );
document.write( "to convert from fahrenheit to celsius, the equation is:<BR>\n" );
document.write( "x = 5/9 * (y - 32)\r<BR>\n" );
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document.write( "to test this out, assume the celsius is 0 degrees.<BR>\n" );
document.write( "to convert to fahrenheit, the formula becomes:<BR>\n" );
document.write( "y = 9/5 * 0 + 32 which results in y = 32<BR>\n" );
document.write( "to convert 32 degrees fahrenheit to celsius, the formula becomes:<BR>\n" );
document.write( "x = 5/9 * (y - 32) which results in x = 5/9 * 0 which results in x = 0.\r<BR>\n" );
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document.write( "on the other end, assume the celsius is 212 degrees.<BR>\n" );
document.write( "to convert to fahrenheit, the formula becomes:<BR>\n" );
document.write( "y = 9/5 * 100 + 32 which results in y = 180 + 32 which results in y = 212.<BR>\n" );
document.write( "to convert 22 degrees fahrenheit to celsius, the formula becomes:<BR>\n" );
document.write( "x = 5/9 * (212 - 32) which results in x = 5/9 * 180) which results in x = 100.\r<BR>\n" );
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document.write( "the formula works at the extremes that we used to derive the formula in the first place.\r<BR>\n" );
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document.write( "it will work in between as well.\r<BR>\n" );
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document.write( "bear in mind that the celsius to fahrenheit conversion is not necessarily a straight line function, so the estimates in between will be close to the actual temperature but not exactly on.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume celsius is 50 degrees.<BR>\n" );
document.write( "fahrenheit is equal to 9/5 * 50 + 32 which is equal to 122 degrees.<BR>\n" );
document.write( "the actual fahrenheit temperature will be near 122 degrees but not necessarily right at 122 degrees.<BR>\n" );
document.write( "the formula will give you an approximation that is close but will not necessarily be right on.\r<BR>\n" );
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document.write( "as far as the equation you showed up top in your problem, i don't understand what that has to do with celsius or fahrenheit.\r<BR>\n" );
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document.write( "the equation is:\r<BR>\n" );
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document.write( "x+10y=2, for y\r<BR>\n" );
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document.write( "it appears you want to solve for y.\r<BR>\n" );
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document.write( "here's how you would do that:\r<BR>\n" );
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document.write( "x + 10y = 2<BR>\n" );
document.write( "subtract x from both sides of the equation to get:<BR>\n" );
document.write( "10y = -x + 2<BR>\n" );
document.write( "divide both sides of the equation by 10 to get:<BR>\n" );
document.write( "y = (1/10) * -x + (1/10) * 2<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "y = -(1/10)x + (1/5)\r<BR>\n" );
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document.write( "your original equation is x + 10y = 2<BR>\n" );
document.write( "after you solved for y, your final equation is y = (-1/10)x + (1/5)\r<BR>\n" );
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document.write( "take any value for x and solve for y in the second equation.<BR>\n" );
document.write( "use those values for x and y in the first equation and you'll see that it becomes a true equation which will confirm the final equation as being a good one.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "i assumed x was equal to 32.<BR>\n" );
document.write( "i chose this number at random.<BR>\n" );
document.write( "i substituted for the value of x in the second equation to get;<BR>\n" );
document.write( "y = (-1/10) * 32 + (1/5) to get y = -3<BR>\n" );
document.write( "i substituted for x and y in the first equation to get:<BR>\n" );
document.write( "x + 10 y = 2 becomes 32 + (10 * -3) = 2 which becomes:<BR>\n" );
document.write( "32 - 30 = 2 which becomes 2 = 2<BR>\n" );
document.write( "this equation is true so the value of 32 for x and -3 for y is good.<BR>\n" );
document.write( "the equation is true means that the values of x and y that we used are solutions to the equation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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