document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074031>Question 1074031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -x+y=3<BR>\n" );
document.write( "4x+4y=9<BR>\n" );
document.write( "Find if these are parallel, perpendicular or neither. <BR>\n" );
document.write( "Is this neither and is this where you substitute 0 for x and y?<BR>\n" );
document.write( "Can someone show me the steps so I can understand? Thanks &#128522; </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688800 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If two lines are parallel, they have the same slope,<BR>\n" );
document.write( "and if two lines have the same slope, they are parallel.<BR>\n" );
document.write( "If two lines are perpendicular, the product of their slopes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and if the product of the slopes of two lines is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the lines are perpendicular.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you solve for y in a linear equation,<BR>\n" );
document.write( "you get the equation in the slope-intercept form,<BR>\n" );
document.write( "and in that form, the coefficient of the x is the slope.<BR>\n" );
document.write( "For example, solving for y in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2By=3 ALIGN=MIDDLE  ALT=\"-x%2By=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B3 ALIGN=MIDDLE  ALT=\"y=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The invisible <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is multiplying x is the slope,<BR>\n" );
document.write( "and the 3 is the y-intercept (or intercept for short).<BR>\n" );
document.write( "That is the y-coordinate of the point where the line crosses the y-axis.<BR>\n" );
document.write( " <BR>\n" );
document.write( "You do not need to solve for y, if all you need is the slope;<BR>\n" );
document.write( "just dividing the coefficients of x and y, and changing the sign is enough.<BR>\n" );
document.write( "For example, if you were to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B4y=9 ALIGN=MIDDLE  ALT=\"4x%2B4y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y, the first step would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-4x%2B9 ALIGN=MIDDLE  ALT=\"4y=-4x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , turning the 4x on the same side as the 4y into -4x on the other side.<BR>\n" );
document.write( "That changed the sign of the b4 that was the coefficient of x.<BR>\n" );
document.write( "The next step would be dividing everything by the 4 multiplying the y,<BR>\n" );
document.write( "and that would leave <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F4=-1 ALIGN=MIDDLE  ALT=\"%28-4%29%2F4=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the slope) as coefficient of x.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Now you know that the slopes of those two lines are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since their product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A%28-1%29=-1 ALIGN=MIDDLE  ALT=\"1%2A%28-1%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the lines are perpendicular. </SPAN>\n" );
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