document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=227363>Question 227363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decide whether the pair line is parallel, perpendicular or neither\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y=5 ALIGN=MIDDLE  ALT=\"2x%2B5y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-2y=10 ALIGN=MIDDLE  ALT=\"5x-2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168978 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=168978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Decide whether the pair line is parallel, perpendicular or neither\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y=5 ALIGN=MIDDLE  ALT=\"2x%2B5y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-2y=10 ALIGN=MIDDLE  ALT=\"5x-2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Two lines are parallel when they have the same slope and two lines are perpendicular when the product of their slopes is -1 or m1*m2=-1 where m1 is the slope of the first line and m2 is the slope of the line perpendicular to the first line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Put above pair of lines in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Let's look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y=5 ALIGN=MIDDLE  ALT=\"2x%2B5y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and put it in slope-intercept form using the following steps.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 2x from both sides of the equation \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y-2x=5-2x ALIGN=MIDDLE  ALT=\"2x%2B5y-2x=5-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=-2x%2B5 ALIGN=MIDDLE  ALT=\"5y=-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Divide by 5 to both sides of the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y%2F5=-2x%2F5%2B5%2F5 ALIGN=MIDDLE  ALT=\"5y%2F5=-2x%2F5%2B5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2F5%2B1 ALIGN=MIDDLE  ALT=\"y=-2x%2F5%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y=5 ALIGN=MIDDLE  ALT=\"2x%2B5y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in slope-intercept form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2F5%2B1 ALIGN=MIDDLE  ALT=\"y=-2x%2F5%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the slope {{m1=-2/5) and y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Let's now look at equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-2y=10 ALIGN=MIDDLE  ALT=\"5x-2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and put it in slope-intercept form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add 2y-10 to both sides of the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-2y%2B2y-10=10%2B2y-10 ALIGN=MIDDLE  ALT=\"5x-2y%2B2y-10=10%2B2y-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-10=2y ALIGN=MIDDLE  ALT=\"5x-10=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Divide by 2 to both sides of the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F2-10%2F2=2y%2F2 ALIGN=MIDDLE  ALT=\"5x%2F2-10%2F2=2y%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F2-5=y ALIGN=MIDDLE  ALT=\"5x%2F2-5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%2F2-5 ALIGN=MIDDLE  ALT=\"y=5x%2F2-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-2y=10 ALIGN=MIDDLE  ALT=\"5x-2y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > in slope-intercept form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%2F2-5 ALIGN=MIDDLE  ALT=\"y=5x%2F2-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=5%2F2 ALIGN=MIDDLE  ALT=\"m2=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  The slopes in Step 4 and 6 are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1=-2%2F5 ALIGN=MIDDLE  ALT=\"m1=-2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=5%2F2 ALIGN=MIDDLE  ALT=\"m2=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The product of their slopes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1%2Am2=%28-2%2F5%29%285%2F2%29=-1 ALIGN=MIDDLE  ALT=\"m1%2Am2=%28-2%2F5%29%285%2F2%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The means the lines are perpendicular.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 8.  ANSWER:  The two given lines are perpendicular.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The graphs of these lines are shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C+-10%2C10%2C-10%2C10%2C+-2x%2F5%2B1%2C+5x%2F2-5%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C+-10%2C10%2C-10%2C10%2C+-2x%2F5%2B1%2C+5x%2F2-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope the above steps were helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And good luck in your studies!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
document.write( "\n" );
document.write( "http://www.FreedomUniversity.TV\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );