document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387629>Question 387629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the lines y = 3x + 7  and x + 2y = -10\r<BR>\n" );
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document.write( "Are the lines parallel? Explain why by comparing the slopes of the lines.\r<BR>\n" );
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document.write( "Are the lines perpendicular? Explain why by comparing the slopes of the lines.\r<BR>\n" );
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document.write( "Do the lines intersect? Explain why. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274020 by </B><A HREF=/tutors/aboutme.mpl?userid=gwendolyn><B>gwendolyn(128)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gwendolyn><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=gwendolyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's put both line equations into slope-intercept form:<BR>\n" );
document.write( "y = mx + b, where m is the slope of the line.\r<BR>\n" );
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document.write( "The first equation is already in the right form:<BR>\n" );
document.write( "y = 3x + 7, so it has a slope of 3.\r<BR>\n" );
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document.write( "The second equation is:<BR>\n" );
document.write( "x + 2y = -10, subtracting x from both sides:<BR>\n" );
document.write( "x + 2y - x = -10 - x<BR>\n" );
document.write( "2y = -10 - x or<BR>\n" );
document.write( "2y = -x - 10 \r<BR>\n" );
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document.write( "And dividing each side by 2 to isolate y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y%2F2+=+%28-x+-+10%29%2F2+ ALIGN=MIDDLE  ALT=\"+2y%2F2+=+%28-x+-+10%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, distributing the division:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-x%2F2+-+10%2F2+ ALIGN=MIDDLE  ALT=\"+y+=+-x%2F2+-+10%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "y = - (1/2)*x - 5<BR>\n" );
document.write( "so the slope of the second line is -1/2\r<BR>\n" );
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document.write( "So the answer to the first question is that the lines are not parallel, since the slopes are not identical.\r<BR>\n" );
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document.write( "Lines are perpendicular if the slopes are negative reciprocals of each other. The negative reciprocal of the first slope (3) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F3%29 ALIGN=MIDDLE  ALT=\"-%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29 ALIGN=MIDDLE  ALT=\"-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the answer to the second question is that the lines are not perpendicular.\r<BR>\n" );
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document.write( "The last question is whether the lines intersect. Since the lines are not parallel (see question 1), they must intersect somewhere (the question doesn't ask us to find where).\r<BR>\n" );
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