document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999176>Question 999176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation in standard form of a line whose x-intercept is an integer and y-intercept is a fraction. Explain how you know that the x-intercept is an integer and y-intercept is a fraction </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616947 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=616947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ax + by = c\r<BR>\n" );
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document.write( "the x-intercept is the value of x when y = 0.<BR>\n" );
document.write( "the y-intercept is the value of y when x = 0.\r<BR>\n" );
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document.write( "when y = 0, ax = c which results in x = c/a\r<BR>\n" );
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document.write( "when x = 0, by = c which results in y = c/b\r<BR>\n" );
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document.write( "in order for c/a to be an integer, c has to be a multiple of a.\r<BR>\n" );
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document.write( "in order for c/b to be a fraction, c must not be a multiple of b.\r<BR>\n" );
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document.write( "if c is a multiple of a, then c can be made equal to a*d, where d is an integer.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "55 / 5 is an integer because 55 is a multiple of 5.<BR>\n" );
document.write( "55 = 5 * 11, so 55/5 = 11\r<BR>\n" );
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document.write( "56 / 5 is not an integer because 56 is not a multiple of 5.\r<BR>\n" );
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document.write( "-15 / 5 is an integer because 15 is a multiple of 5.<BR>\n" );
document.write( "15 = 5 * 3, so 15/5 = 3\r<BR>\n" );
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document.write( "-16 / 5 is not an integer because 16 is not a multiple of 5.\r<BR>\n" );
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document.write( "so, if you want ax + by = c to have the x-intercept an integer and the y-intercept a fraction, then c must be a multiple of a but not a multiple of b.\r<BR>\n" );
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document.write( "an example would be:\r<BR>\n" );
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document.write( "5x + 6y = 15\r<BR>\n" );
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document.write( "the x intercept is the value of x when y = 0.<BR>\n" );
document.write( "when y = 0, the equation becomes 5x = 15.<BR>\n" );
document.write( "solve for x to get x = 15/5 = 3.<BR>\n" );
document.write( "3 is an integer.\r<BR>\n" );
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document.write( "the y intercept is the value of y when x = 0.<BR>\n" );
document.write( "when x = 0, the equation becomes 6y = 15.<BR>\n" );
document.write( "solve for y to get y = 15/6.<BR>\n" );
document.write( "15/6 is not an integer.\r<BR>\n" );
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document.write( "that's my take.\r<BR>\n" );
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document.write( "an integer can also be described as a fraction where the denominator is equal to 1.\r<BR>\n" );
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document.write( "why is 55/5 an integer?\r<BR>\n" );
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document.write( "multiply numerator and denominator of 55/5 by 1/5 and you get (55*1/3) / (5*1/5) which results in 11/1 which is the same as 11.\r<BR>\n" );
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document.write( "55/5 is therefore an integer because it can be simplified to a ratio where the denominator is equal to 1.\r<BR>\n" );
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document.write( "56/5 cannot be simplified to a ratio where the numerator is an integer and the denominator is equal to 1.\r<BR>\n" );
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document.write( "this is because 56 is not a multiple of 5.\r<BR>\n" );
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document.write( "you can find a number such that the denominator is 1, but the number will not be an integer.\r<BR>\n" );
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document.write( "56/5 = 11.2/1 = 11.2 which is a fraction in decimal form.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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