document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213539>Question 213539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the distance between the lines with equations y=3x-9 and y = 3x - 4.\r<BR>\n" );
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document.write( "a)5/4<BR>\n" );
document.write( "b)5 sqrt(10)/2<BR>\n" );
document.write( "c)sqrt(10)/2<BR>\n" );
document.write( "d)13 sqrt(10)/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161347 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=161347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the distance between the lines with equations 3x - y = 9 and y = 3x - 4.\r<BR>\n" );
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document.write( "a)5/4<BR>\n" );
document.write( "b)5 sqrt(10)/2<BR>\n" );
document.write( "c) sqrt(10)/2<BR>\n" );
document.write( "d) 13 sqrt(10)/2\r<BR>\n" );
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document.write( "Step 1.  Here's a graph of the two equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+y=3x-9%2C+y=3x-4%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+y=3x-9%2C+y=3x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2.  We need a line that's perpendicular to the two parallel lines and then use the point where it intercepts the axis.  The slope of the above two lines is 3 and the perpendicular line has a slope of -1/3.  The reason being is the fact that the product of the slope for two perpendicular lines is equal to -1.\r<BR>\n" );
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document.write( "Step 3.  So let's pass the perpendicular line  through (0,-4) and then we need to solve y=3x-4 line and figure out where it intersects the the other parallel line.\r<BR>\n" );
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document.write( "So our equation in slope intercept form is  y=mx+b=-4=-0/3+b. So b=-4.  The the equation of the perpendicular line is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2Ax%2F3%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-1%2Ax%2F3%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here a graph of the situation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+y=3x-4%2C+y=3x-9%2C+y=%28-x%2F3%29-4%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+y=3x-4%2C+y=3x-9%2C+y=%28-x%2F3%29-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  For visually simplicity, let's pick a point say (0,-4) as one point. We can find the other point, using a system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-x%2F3%29-4 ALIGN=MIDDLE  ALT=\"y=%28-x%2F3%29-4\"   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=3x-9 ALIGN=MIDDLE  ALT=\"y=3x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The following steps will solve this system of equations\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=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++0.333333333333333%5Cx+%2B+1%5Cy+=+-4%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+-9+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.333333333333333%2Ax+=+-4+-+1%2Ay ALIGN=MIDDLE  ALT=\"0.333333333333333%2Ax+=+-4+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333 ALIGN=MIDDLE  ALT=\"x+=+-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2A%28-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333%29+%2B+1%5Cy+=+-9 ALIGN=MIDDLE  ALT=\"-3%2A%28-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333%29+%2B+1%5Cy+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=-4.5. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333 ALIGN=MIDDLE  ALT=\"x+=+-4%2F0.333333333333333+-+1%2Ay%2F0.333333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=1.5.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=1.5%2C+y=-4.5+%29 ALIGN=MIDDLE  ALT=\"system%28+x=1.5%2C+y=-4.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Step 5.  Based on the above the other point (1.5 and -4.5)\r<BR>\n" );
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document.write( "Step 6.  The distance between (0,-4) and (1.5, -4.5) is therefore,  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%280-1.5%29%5E2%2B%28-4-%28-4.5%29%29%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%280-1.5%29%5E2%2B%28-4-%28-4.5%29%29%29\"   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=d=sqrt%282.25%2B0.25%29 ALIGN=MIDDLE  ALT=\"d=sqrt%282.25%2B0.25%29\"   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=d=sqrt%282.5%29=sqrt%2810%2F4%29%29 ALIGN=MIDDLE  ALT=\"d=sqrt%282.5%29=sqrt%2810%2F4%29%29\"   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=d=sqrt%2810%29%2F2 ALIGN=MIDDLE  ALT=\"d=sqrt%2810%29%2F2\"   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=d=1.58 ALIGN=MIDDLE  ALT=\"d=1.58\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7.  The answer is c or 1.58.\r<BR>\n" );
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document.write( "I hope the above steps were helpful and it's probably long.  I'll see if there is a shorter way.  But that's my approach  for now.\r<BR>\n" );
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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" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( " </SPAN>\n" );
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