document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=718316>Question 718316</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "I am trying to graph an absolute value equation and cannot seem to solve it.<BR>\n" );
document.write( "the equation is to Solve  |2x+2|=-2/3x+2 Graphically.<BR>\n" );
document.write( "In my answer booklet it says the 2 answer to this absolute value equation is x=-3 and x=0 but when I plot these two equations i notice that they both have a y intercept of 2 so, i thought that they would meet at x=2. Please help me, it would be greatly appreciated! Best of Luck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440954 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=440954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, please put fractions which are factors in parentheses. The right side, as you posted it, means:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3x%2B2 ALIGN=MIDDLE  ALT=\"-2%2F3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It was only your mention that the y-intercept was 2 that allowed me to figure out that it was supposed to be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "description that the <br>At the y-intercept of 2, the y-coordinate is 2. The x-coordinate on the y-axis is always 0. This explains the x=0 solution.<br><BR>\n" );
document.write( "As for the other solution...<BR>\n" );
document.write( "The graphs of equations of the form:<BR>\n" );
document.write( "y = | mx+b |<BR>\n" );
document.write( "will \"bounce\" off the x-axis. They will \"bounce\" at the point whose x-coordinate is the number that makes mx+b be zero. For y = | 2x+2 |, the graph will \"bounce\" off the x-axis at -1 because -1 makes 2x+2 be zero. (If you can't see this, just set 2x+2 = 0 and solve for x.)<br><BR>\n" );
document.write( "The graph of y = | mx + b | will be the graphs of two \"half-lines\" which meet at the \"bounce\" point. One \"half-line\" will the part of the graph of y = mx+b that is above the x-axis and the other \"half-line\" will the the part of the graph of y = -(mx+b) (or y - -mx-b) which is above the x-axis.<br><BR>\n" );
document.write( "For y = | 2x+2 |, the two \"half-lines\" would be: y = 2x+2 and y = -2x-2. The first \"half-line\" is the one whose y-intercept is 2 and intersects <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2F3%29x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2F3%29x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > there. The other \"half-line\", y = -2x-2, will intersect <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2F3%29x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2F3%29x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > somewhere to the left of the \"bounce\" point at (-1, 0).<br><BR>\n" );
document.write( "Here's a graph of both y = | 2x+2 | and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2F3%29x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2F3%29x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C+400%2C+-5%2C+5%2C+-2%2C+8%2C+abs%282x%2B2%29%2C+%28-2%2F3%29x+%2B+2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C+400%2C+-5%2C+5%2C+-2%2C+8%2C+abs%282x%2B2%29%2C+%28-2%2F3%29x+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );