document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204229>Question 1204229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a line has an x-intercept at x=4 and a y-intercept at y=-2 find its equation in the form y=mx+b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840346 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Method 1\r<BR>\n" );
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document.write( "The x-intercept always happens when y = 0.<BR>\n" );
document.write( "The y-intercept always happens when x = 0.\r<BR>\n" );
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document.write( "This means an x-intercept of 4 and y-intercept of -2 produces the points (4,0) and (0,-2)\r<BR>\n" );
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document.write( "Let's find the slope of the line through them.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C15%2C%22Given%22%2C%22points%3A%22%2C%22%28%22%2Cx%5B1%5D%2C%22%2C%22%2Cy%5B1%5D%2C%22%29+=+%22%2C%22%284%2C0%29%22%2C%22and%22%2C%22%28%22%2Cx%5B2%5D%2C%22%2C%22%2Cy%5B2%5D%2C%22%29+=+%22%2C%22%280%2C-2%29%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+slope+=+rise%2Frun+=+matrix%281%2C3%2C%22change%22%2C%22in%22%2C%22y%22%29%2Fmatrix%281%2C3%2C%22change%22%2C%22in%22%2C%22x%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-2+-+0%29%2F%280+-+4%29 ALIGN=MIDDLE  ALT=\"m+=+%28-2+-+0%29%2F%280+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-2%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"m+=+%28-2%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1%2F2 ALIGN=MIDDLE  ALT=\"m+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope is 1/2.<BR>\n" );
document.write( "It means \"go up 1, then right 2\".\r<BR>\n" );
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document.write( "The y-intercept is b = -2 as mentioned earlier.\r<BR>\n" );
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document.write( "We will go from the template y = mx+b to the <font color=red size=4>final answer  y = (1/2)x - 2</font>\r<BR>\n" );
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document.write( "This is the same as writing either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F2%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+expr%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y+=+expr%281%2F2%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Optionally you could replace 1/2 with 0.5, but I don't think that slope is as helpful since 1/2 means \"up 1, right 2\". It might be tricky to convey that with 0.5\r<BR>\n" );
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document.write( "Method 2\r<BR>\n" );
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document.write( "Let 'a' and b represent the x and y intercepts. <BR>\n" );
document.write( "Neither value can be zero.\r<BR>\n" );
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document.write( "The aptly named intercept form is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fa+%2B+y%2Fb+=+1 ALIGN=MIDDLE  ALT=\"x%2Fa+%2B+y%2Fb+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This form allows us to quickly spot the x and y intercepts without having to do any math.\r<BR>\n" );
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document.write( "Since the x-intercept happens when y = 0, it leads to,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fa+%2B+0%2Fb+=+1 ALIGN=MIDDLE  ALT=\"x%2Fa+%2B+0%2Fb+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fa+%2B+0+=+1 ALIGN=MIDDLE  ALT=\"x%2Fa+%2B+0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fa+=+1 ALIGN=MIDDLE  ALT=\"x%2Fa+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a%2A1 ALIGN=MIDDLE  ALT=\"x+=+a%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a ALIGN=MIDDLE  ALT=\"x+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We have shown that when y = 0, it produces x = a. <BR>\n" );
document.write( "Therefore the x-intercept is located at (a,0)<BR>\n" );
document.write( "Similar steps will show that the y-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fa+%2B+y%2Fb+=+1 ALIGN=MIDDLE  ALT=\"x%2Fa+%2B+y%2Fb+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is (0,b)\r<BR>\n" );
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document.write( "In this case a = 4 and b = -2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4+-+y%2F2+=+1 ALIGN=MIDDLE  ALT=\"x%2F4+-+y%2F2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28x%2F4+-+y%2F2%29+=+4%2A1 ALIGN=MIDDLE  ALT=\"4%2A%28x%2F4+-+y%2F2%29+=+4%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 4 to clear out the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y+=+4 ALIGN=MIDDLE  ALT=\"x-2y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y+=+4-x ALIGN=MIDDLE  ALT=\"-2y+=+4-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-x%2B4%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"y+=+%28-x%2B4%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-x%29%2F%28-2%29%2B%284%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"y+=+%28-x%29%2F%28-2%29%2B%284%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F2%29x+-+2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F2%29x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We arrive at the same answer found back in the previous method.<BR>\n" );
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