document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123620>Question 123620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am suppose to draw the graph of each line using its y-intercept and its slope..I have gone over the chapter and am just confused on how exactly i find that using this equation. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=9 ALIGN=MIDDLE  ALT=\"4x%2B3y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > I am so ready to tear my hair out...can someone help?\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90683 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=90683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One way to do this problem is to rearrange the given equation into the slope-intercept<BR>\n" );
document.write( "form. The slope-intercept form of an equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b+ ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which m, the multiplier of the x, will be the slope and b, a constant, is the value on<BR>\n" );
document.write( "the y-axis where the graph intercepts (crosses) the y-axis.<BR>\n" );
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document.write( "For this problem you were given the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+3y+=+9 ALIGN=MIDDLE  ALT=\"4x+%2B+3y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To get this equation into the slope-intercept form, let's solve it for y.<BR>\n" );
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document.write( "Begin by getting rid of the 4x term on the left side, so that only the term containing y<BR>\n" );
document.write( "remains on the left side. You can do this by subtracting 4x from both sides. When you <BR>\n" );
document.write( "subtract 4x from the left side the 4x on the left side goes away. And when you subtract 4x<BR>\n" );
document.write( "from the right side you get a -4x on the right side. This means your equation has become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+-4x+%2B+9 ALIGN=MIDDLE  ALT=\"3y+=+-4x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then to solve for y, you just divide both sides of the equation by 3. On the left side<BR>\n" );
document.write( "dividing 3y by 3 results in the left side becoming just y. And on the right side you divide<BR>\n" );
document.write( "both terms by 3. This division makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-4%2F3%29x+%2B+9%2F3 ALIGN=MIDDLE  ALT=\"y+=+%28-4%2F3%29x+%2B+9%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally recognize that the 9 divided by 3 on the right side is just 3. Therefore, the<BR>\n" );
document.write( "equation finally becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-4%2F3%29x+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+%28-4%2F3%29x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that this equation is in the slope-intercept form. The left side is just y. On the right<BR>\n" );
document.write( "side the multiplier of the x is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F3%29 ALIGN=MIDDLE  ALT=\"%28-4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that is the slope. And the constant term<BR>\n" );
document.write( "of +3 is the value on the y-axis that the graph crosses through.<BR>\n" );
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document.write( "One thing you can immediately tell is that the slope is negative which means that in going<BR>\n" );
document.write( "from the left to the right the graph slopes down. And since the slope is defined as the<BR>\n" );
document.write( "change in the value of y divided by the change in the value of x, from the fraction<BR>\n" );
document.write( "-4 divided by 3 that y will go down 4 units for every 3 units that x goes to the right. You<BR>\n" );
document.write( "already know that the point +3 on the y-axis (the point (0, +3) is on the graph. Put your<BR>\n" );
document.write( "pencil on that point. Then move your pencil horizontally to the right 3 units. At that point<BR>\n" );
document.write( "go vertically down 4 units. Stop there and make a mark. That is a second point on the graph.<BR>\n" );
document.write( "[You should be at the point (3, -1)]. You can now extend a straight line through the two points. <BR>\n" );
document.write( "That line will be the graph you are looking for.<BR>\n" );
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document.write( "At this point you should have a graph that looks like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-4%2F3%29x+%2B+3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-4%2F3%29x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to see how to convert equations to slope-intercept form and how to<BR>\n" );
document.write( "make a graph once you have the equation in slope intercept form.<BR>\n" );
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document.write( "A couple of final comments. If your slope intercept equation has an integer (whole number) <BR>\n" );
document.write( "as the multiplier of x, when you think of the slope put that integer over 1.<BR>\n" );
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document.write( "For example, suppose the slope intercept form of the equation was:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x+-+7 ALIGN=MIDDLE  ALT=\"y+=+3x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(I just made this up as an example. It has nothing to do with the problem you were given<BR>\n" );
document.write( "to work.)<BR>\n" );
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document.write( "You would know that the graph crosses the y-axis at -7. And you would also know that the<BR>\n" );
document.write( "slope is +3/1 ... meaning that for every horizontal change of 1 unit to the right, the graph<BR>\n" );
document.write( "would go vertically up 3 units. For this made up example the graph would look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%283%29x+-7%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%283%29x+-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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