document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280564>Question 280564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the equation and identify the y-intercept: 4y+5x= -12. The y-intercept is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203944 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=203944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, get the equation into slope-intercept form:  y = mx + b<BR>\n" );
document.write( "4y + 5x = -12<BR>\n" );
document.write( "subtract 5x from both sides<BR>\n" );
document.write( "4y = -5x -12<BR>\n" );
document.write( "divide both sides by 4<BR>\n" );
document.write( "y = -5/4x -12/3<BR>\n" );
document.write( "y = -5/4x -4<BR>\n" );
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document.write( "Recall, <BR>\n" );
document.write( "the x-intercept is the point where y=0 and<BR>\n" );
document.write( "the y-intercept is the point where x=0.<BR>\n" );
document.write( "Thinking visually, the point (0, ??) will be on y-axis somewhere; likewise the point (??, 0) will be on the x-axis somewhere.  Since we're drawing a line, it will cross at these points.<BR>\n" );
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document.write( "To find the y-intercept, simply set x=0:<BR>\n" );
document.write( "the y-intercept is -4, which is at the point (0,-4)<BR>\n" );
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document.write( "Thinking about the slope-intercept equation, we know the slope is the coefficient of x.<BR>\n" );
document.write( "In this case the slope is -5/4, which means it slopes downward from the upper left to the lower right.<BR>\n" );
document.write( "We can find the x-intercept by setting y=0 and working it out.<BR>\n" );
document.write( "0 = -5/4x -4<BR>\n" );
document.write( "adding 5/4x to both sides<BR>\n" );
document.write( "5/4x = -4<BR>\n" );
document.write( "multiply both sides by 4<BR>\n" );
document.write( "5x = -16<BR>\n" );
document.write( "divide both sides by 5<BR>\n" );
document.write( "x = -16/5<BR>\n" );
document.write( "so the x-intercept is (-16/5, 0)<BR>\n" );
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document.write( "Now you have two points:  (0,-4) and (-16/5,0).<BR>\n" );
document.write( "With two points you can draw line.<BR>\n" );
document.write( "Plot the two points and graph the equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-5%2C5%2C-5%2C5%2C-5%2F4%2Ax+-4%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-5%2C5%2C-5%2C5%2C-5%2F4%2Ax+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A good check is to find another point and verify it is on the line.<BR>\n" );
document.write( "Say x= -4, which neatly cancels the denominator...<BR>\n" );
document.write( "y = -5/4(-4) -4<BR>\n" );
document.write( "y = 20/4 -4<BR>\n" );
document.write( "y = 5 -4<BR>\n" );
document.write( "y = 1<BR>\n" );
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document.write( "Is the point (-4,1) on the line?<BR>\n" );
document.write( "Yes, it is.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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