document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698789>Question 698789</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line, in the form y = mx + b, that is parallel to the line 2x + 3y = 12, and passes through the origin.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you so much for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431060 by </B><A HREF=/tutors/aboutme.mpl?userid=Simnepi><B>Simnepi(216)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Simnepi><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=Simnepi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The form y = mx + b gives the equation of a straight line where m is the slope of the line(the gradient) and b is the intercept of the line and the y axis.<BR>\n" );
document.write( "All lines with the same gradient (i.e. the same number in front of the x) are parallel.<BR>\n" );
document.write( "First, let's rearrange your line equation into the correct form of y = mx + b<BR>\n" );
document.write( "2x + 3y = 12<BR>\n" );
document.write( "take the x term across the equals sign (and change its sign as we do so)<BR>\n" );
document.write( "3y = -2x + 12<BR>\n" );
document.write( "Now divide by 3 (across the whole equation) to get rid of the 3y and just leave y<BR>\n" );
document.write( "so<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 4<BR>\n" );
document.write( "Now we can find the equation of the new line.<BR>\n" );
document.write( "The line we want to find has a gradient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (remember? parallel lines have the same gradient!)<BR>\n" );
document.write( "The intercept of the line we want is at (0,0) the origin. so the y intercept = 0<BR>\n" );
document.write( "writing the whole equation of the line we want ......<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x (you could write +0 but there really is no point!)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );