document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75806>Question 75806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the Equation of each line\r<BR>\n" );
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document.write( "x intercept=4  y interccept = -3\r<BR>\n" );
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document.write( "Thanks!\r<BR>\n" );
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document.write( "T </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54431 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x intercept = 4 & y intercept = -3<BR>\n" );
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document.write( "A form of equation that can be used to represent the equation of the line that has a y intercept<BR>\n" );
document.write( "of -3 and an x intercept of +4 is the slope intercept form.  This form is:<BR>\n" );
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document.write( "y = mx + b <BR>\n" );
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document.write( "where m is the slope of the line and b is the y intercept.<BR>\n" );
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document.write( "The problem tells us that the y intercept is -3. This is half of the information that we<BR>\n" );
document.write( "need ... it is the b that we are looking for.  When we put this into the equation form it<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "y = mx - 3<BR>\n" );
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document.write( "All we have to do now is find the slope m.  We can do this in a couple of different<BR>\n" );
document.write( "ways. One of the ways is to make a quick sketch of a coordinate system.  Put a dot on<BR>\n" );
document.write( "the y-axis at -3.  Then go to the x-axis and put a dot at +4. (Those dots represent<BR>\n" );
document.write( "the x and y intercepts that are given in the problem.) Start at the dot on the y axis. <BR>\n" );
document.write( "Note that you have to go horizontally to the right 4 units to be under the dot on the<BR>\n" );
document.write( "x-axis. Also note that you then have to go up 3 units to get to the dot on the x-axis.<BR>\n" );
document.write( "That's all the information we need ... +4 to the right and then +3 up to get the dot on the<BR>\n" );
document.write( "x-axis.  The slope is the vertical change (+3) divided by the horizontal change (+4).<BR>\n" );
document.write( "This is 3/4 and we can substitute this for m in the slope intercept equation that we<BR>\n" );
document.write( "have so far.  This makes the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29x+-+3 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and that's an equation for the line that has the given intercepts.<BR>\n" );
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document.write( "Note that we could also get m (the slope) by identifying the two known points on the line.<BR>\n" );
document.write( "The intercept points in coordinate form are the y intercept (0, -3) and the x intercept (4, 0).<BR>\n" );
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document.write( "Call (0, -3) the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+y%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The corresponding parts are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-3 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Similarly call (4, 0) the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+y%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D+y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the<BR>\n" );
document.write( "corresponding parts are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+0 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The equation for the slope is:<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;\" ><BR>\n" );
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document.write( "Just substitute the values that we defined above. When we do, the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%280+-+%28-3%29%29%2F%284+-+0%29 ALIGN=MIDDLE  ALT=\"m+=+%280+-+%28-3%29%29%2F%284+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+3%2F4 ALIGN=MIDDLE  ALT=\"m+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "And this is exactly what we found previously. So using this method would also give us<BR>\n" );
document.write( "the slope intercept equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29x+-+3 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this gives you some insight into finding an equation for a line that is defined<BR>\n" );
document.write( "by two points ... the x and y intercepts. </SPAN>\n" );
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