document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135207>Question 1135207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My math teacher has asked us this one complex question for points, just for fun, but it counts for points.  Can someone help?  I'm so stressed out!\r<BR>\n" );
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document.write( "Consider an equation of a line written in standard form:  4x  -  2y  =  8. Also consider a point (4, 2) that is not on that line.<BR>\n" );
document.write( "(a) Find the equation of the line that is parallel to 4x  -  2y  =  8  and passes through the point ( 4, 2).<BR>\n" );
document.write( "      Write the equation is all four forms: slope-intercept, point-slope, standard, and two-point forms.<BR>\n" );
document.write( "(b) Find the equation of the line that is perpendicular to 4x  -  2y  =  8  and passes through the point ( 4, 2).<BR>\n" );
document.write( "      Write the equation is all four forms: slope-intercept, point-slope, standard, and two-point forms.<BR>\n" );
document.write( "(c) Graph all three lines on the same coordinate axis.<BR>\n" );
document.write( "      For all three lines, graph four (4) points for each line; twelve (12) points and three (3) lines total.<BR>\n" );
document.write( "      The first point is (4, 2), the second point is of your choosing, and the third & fourth points are<BR>\n" );
document.write( "       the two intercepts (vertical and horizontal); note that (4, 2) is not on the original given line so pick another point on the first line. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752779 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=752779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) Find the equation of the line that is parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-2y+=+8 ALIGN=MIDDLE  ALT=\"4x+-2y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and passes through the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4 ALIGN=MIDDLE  ALT=\"+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "recall: parallel lines have same slope\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+2y+=+8 ALIGN=MIDDLE  ALT=\"4x+-+2y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...write in slope intercept form; means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=mx%2Bb ALIGN=MIDDLE  ALT=\"+y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is aslope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is y-intercept\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-8=+2y+ ALIGN=MIDDLE  ALT=\"4x+-8=+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F2+-+8%2F2=+y+ ALIGN=MIDDLE  ALT=\"4x%2F2+-+8%2F2=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x+-4+ ALIGN=MIDDLE  ALT=\"y=2x+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>slope-intercept form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4 ALIGN=MIDDLE  ALT=\"b=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use point-slope form and given point to find equation of the parallel line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=4 ALIGN=MIDDLE  ALT=\"x%5B1%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=2 ALIGN=MIDDLE  ALT=\"y%5B1%5D=2\"   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=y-2=2%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2=2%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->point-slope form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=2x-8 ALIGN=MIDDLE  ALT=\"y-2=2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-8%2B2 ALIGN=MIDDLE  ALT=\"y=2x-8%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-6 ALIGN=MIDDLE  ALT=\"y=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>slope-intercept form of your equation of the parallel line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=6 ALIGN=MIDDLE  ALT=\"2x-y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >->standard form\r<BR>\n" );
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document.write( " a  line passing through the points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   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=x%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+2 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+-6 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >->  your y-intercept  \r<BR>\n" );
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document.write( "Linear equation passing through two point is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D+%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D+%29%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> two-point form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+%28-6-2%29%2F%280-4+%29%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2+=+%28-6-2%29%2F%280-4+%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+%28-8%2F-4+%29%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2+=+%28-8%2F-4+%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=2%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2+=2%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) Find the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+2y+=+8 ALIGN=MIDDLE  ALT=\"4x+-+2y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and passes through the point ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "recall: perpendicular lines have  slopes negative reciprocal to each other\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+8=+2y+ ALIGN=MIDDLE  ALT=\"4x+-+8=+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F2+-8%2F2=+y+ ALIGN=MIDDLE  ALT=\"4x%2F2+-8%2F2=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x+-4+ ALIGN=MIDDLE  ALT=\"y=2x+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>slope-intercept form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>  perpendicular line will have a slope<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2F2 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use point-slope form and given point to find equation of the parallel line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%5Bp%5D%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%5Bp%5D%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2F2 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=y-2=%28-1%2F2%29%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2=%28-1%2F2%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=%28-1%2F2%29x%2B2 ALIGN=MIDDLE  ALT=\"y-2=%28-1%2F2%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29x%2B2%2B2 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29x%2B2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->slope-intercept\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-x%2B8 ALIGN=MIDDLE  ALT=\"2y=-x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=8 ALIGN=MIDDLE  ALT=\"x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >->standard form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+2 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->  your y-intercept  \r<BR>\n" );
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document.write( "Linear equation passing through two point is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D+%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D+%29%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> two-point form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+%284-2%29%2F%280-4+%29%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2+=+%284-2%29%2F%280-4+%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=+%282%2F-4+%29%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2+=+%282%2F-4+%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2+=-%281%2F2%29%28x-4%29 ALIGN=MIDDLE  ALT=\"y-2+=-%281%2F2%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "(c) Graph all three lines on the same coordinate axis.\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+10%2C+2x+-+4%2C2x-6%2C+-%281%2F2%29%28x-4%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+4%2C2x-6%2C+-%281%2F2%29%28x-4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );