document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203432>Question 1203432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A line k passes through the points ​(−5​,−8​) and ​(1,34​). A second line h passes through the points ​(−3​,−27​) and ​(3​,15​). Is line k parallel to line​ h? Why or why​ not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838990 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > passes through the points ​(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >​,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   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;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34 ALIGN=MIDDLE  ALT=\"34\"   DISABLED_style= \"max-width:90%; height:auto;\" >​).\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=find_equation_of_line.solver>FIND EQUATION of straight line given 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-5, -8) and (x2, y2) = (1, 34).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%2834--8%29%2F%281--5%29+=+7 ALIGN=MIDDLE  ALT=\"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%2834--8%29%2F%281--5%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A-5+%2Bb+=+27 ALIGN=MIDDLE  ALT=\"7%2A-5+%2Bb+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8-7%2A-5+=+27 ALIGN=MIDDLE  ALT=\"b=-8-7%2A-5+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  y=(7)x + (27)<BR>\n" );
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document.write( "  Your graph:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+7%2Ax%2B27+%29%2C%0D%0A++++red%28+locate%28+-5%2C+-8%2C+%22-5%2C+-8%22+%29%2C+circle%28+-5%2C+-8%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+1%2C+34%2C+%221%2C+34%22+%29%2C+circle%28+1%2C+34%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "line h passes through the points ​(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >​,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27%E2%80%8B ALIGN=MIDDLE  ALT=\"-27%E2%80%8B\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and ​(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%E2%80%8B ALIGN=MIDDLE  ALT=\"3%E2%80%8B\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >​)\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=find_equation_of_line.solver>FIND EQUATION of straight line given 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-3, -27) and (x2, y2) = (3, 15).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%2815--27%29%2F%283--3%29+=+7 ALIGN=MIDDLE  ALT=\"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%2815--27%29%2F%283--3%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A-3+%2Bb+=+-6 ALIGN=MIDDLE  ALT=\"7%2A-3+%2Bb+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-27-7%2A-3+=+-6 ALIGN=MIDDLE  ALT=\"b=-27-7%2A-3+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  y=(7)x + (-6)<BR>\n" );
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document.write( "  Your graph:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+7%2Ax%2B-6+%29%2C%0D%0A++++red%28+locate%28+-3%2C+-27%2C+%22-3%2C+-27%22+%29%2C+circle%28+-3%2C+-27%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+3%2C+15%2C+%223%2C+15%22+%29%2C+circle%28+3%2C+15%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so, a line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7x+%2B+27+ ALIGN=MIDDLE  ALT=\"y=7x+%2B+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and a line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+ ALIGN=MIDDLE  ALT=\"h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7x+-6 ALIGN=MIDDLE  ALT=\"y=7x+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see, both lines have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+slope ALIGN=MIDDLE  ALT=\"+slope\"   DISABLED_style= \"max-width:90%; height:auto;\" >, therefore lines  are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+30%2C+7x+%2B+27%2C+7x+-6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+30%2C+7x+%2B+27%2C+7x+-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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