document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=491974>Question 491974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We had a seat work in class in which the instructions was to write an equation of a linear function given the following conditions:<BR>\n" );
document.write( "the first was Given a slope and intercept..<BR>\n" );
document.write( "My final answer was in the form y= mx + b but my teacher made it wrong. she told us that it must be in the form ax + by = c. I scanned my notes to make sure that what i am telling is right. I found out that my teacher gave us a seatwork in whch the given equations were in the form y= mx + b and the instructions was \" Rewrite the following linear functions in standard form.\" \r<BR>\n" );
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document.write( "Please help me, what should I do? Are my answers correct or wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334918 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=334918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the slope intercept form of a linear equation is y = mx + b\r<BR>\n" );
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document.write( "the standard form of a linear equation is ax + by = c\r<BR>\n" );
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document.write( "suppose your equation was:\r<BR>\n" );
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document.write( "2x + 3y = 15\r<BR>\n" );
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document.write( "that's in standard form with a = 2 and b = 3 and c = 15\r<BR>\n" );
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document.write( "subtract 2x from both sides of the equation to get:\r<BR>\n" );
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document.write( "3y = -2x + 15\r<BR>\n" );
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document.write( "divide both sides of the equation by 3 to get:\r<BR>\n" );
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document.write( "y = (-2/3)x + 15/3 which becomes:\r<BR>\n" );
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document.write( "y = (-2/3)x + 5\r<BR>\n" );
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document.write( "that's the slope intercept form of the equation.\r<BR>\n" );
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document.write( "the slope intercept form is y = mx + b\r<BR>\n" );
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document.write( "m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "in this equation, the slope is equal to (-2/3) and the y-intercept is equal to 5.\r<BR>\n" );
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document.write( "to convert back to the standard form of the equation, do the following:\r<BR>\n" );
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document.write( "you start from y = (-2/3)x + 5\r<BR>\n" );
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document.write( "add (-2/3)x to both sides of the equation to get:\r<BR>\n" );
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document.write( "(2/3)x + y = 5\r<BR>\n" );
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document.write( "multiply both sides of the equation by 3 to get:\r<BR>\n" );
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document.write( "2x + 3y = 15\r<BR>\n" );
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document.write( "you're back to the standard form of your equation.\r<BR>\n" );
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document.write( "these forms are equivalent.\r<BR>\n" );
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document.write( "2x + 3y = 15 is equivalent to y = -(2/3)x + 5\r<BR>\n" );
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document.write( "just supply a random value for x and solve for y in both equations.\r<BR>\n" );
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document.write( "let x = 3.\r<BR>\n" );
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document.write( "2x + 3y = 15 becomes 6 + 3y = 15 which becomes 3y = 9 which becomes y = 3.\r<BR>\n" );
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document.write( "y = (-2/3)x + 5 becomes y = (-2/3)*3 + 5 which becomes y = -2 + 5 which becomes y = 3.\r<BR>\n" );
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document.write( "you get y = 3 in both cases, confirming the fact that the 2 equations are equivalent.\r<BR>\n" );
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document.write( "any other value of x will confirm the same.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = 20, 2x + 3y = 15 becomes 40 + 3y = 15 which becomes 3y = -25 which becomes y = -25/3\r<BR>\n" );
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document.write( "y = (-2/3)x + 5 becomes y = (-2/3)*20 + 5 which becomes y = -40/3 + 5 which becomes y = -40/3 + 15/3 which becomes -25/3.\r<BR>\n" );
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document.write( "y is the same value in both equations, confirming again that the equations are equivalent.\r<BR>\n" );
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document.write( "just follow the steps to convert from the slope intercept form of the equation to the standard form of the equation and you should be ok.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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