document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=396931>Question 396931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm working on the Linear Equations in my Alegbra book. I have a graph with a horizontal X line and a vertical Y line. There is a line that slopes down from left to right. My problem is asking me to find the slope, the y-intercept, and write the equation. \r<BR>\n" );
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document.write( "The line intercepts the Y line at 1, then the X line at 2. I figured the slope is -1/2 since {delta y = -2} & {delta x = 4}. I believe the y-intercept is just 2, but I'm totally questioning myself on this & have no idea how to write the equation. Can you help me please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281425 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=281425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let's start by using the correct words to describe things.  Not the X-line or Y-line, it is the x-axis and the y-axis.\r<BR>\n" );
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document.write( "If the line crosses the y-axis at 1, then the coordinates of that point are (0,1).  If the line crosses the x-axis at 2, then the coordinates of that point are (2,0).\r<BR>\n" );
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document.write( "The slope of your line is indeed <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{1}{2}\">.  Use the slope formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} \">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_2,y_2\right)\"> are the coordinates of two points on your line.  We determined the coordinates of two points by using the intercept values, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{1\ -\ 0}{0\ -\ 2}\ =\ -\frac{1}{2}\">\r<BR>\n" );
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document.write( "I'm not sure where you got the idea that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta x\ =\ 4\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta y\ =\ -2\"> unless there is another point or two defined on your line that you didn't tell us about.  Using the coordinate differences on the two intercepts (reading left to right), <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta x\ =\ 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta y\ =\ -1\">\r<BR>\n" );
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document.write( "Once you have the slope and the y-coordinate value of the y-intercept, writing an equation that represents the line is easy.  You have the information to write your equation in slope-intercept form, namely \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ mx\ +\ b\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the slope number and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> is the y-coordinate of the y-intercept.  For your problem, that is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\ =\ -\frac{1}{2}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ 1\">, hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{1}{2}x\ +\ 1\">\r<BR>\n" );
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document.write( "From there you can use a little algebra to put the equation into Standard form, namely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ Ax\ +\ By\ =\ C\">\r<BR>\n" );
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document.write( "For you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 2y\ =\ 2\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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