document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849726>Question 849726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance between the two parallel lines given by the equation: 5x-4y=22 and -75x=150-60y\r<BR>\n" );
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document.write( "the instructions given by the teacher were:<BR>\n" );
document.write( "1. put both equations in y=mx+b form<BR>\n" );
document.write( "2. find a point (x,y) on either equation<BR>\n" );
document.write( "3. find equation of the perpendicular line that passes through (x,y)<BR>\n" );
document.write( "4. use systematic equation to solve with equation 3 (the new one) and the one that wasn't used to get the point in step 2<BR>\n" );
document.write( "5. calculate with distance formula\r<BR>\n" );
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document.write( "I don't know how to continue after solving both equations for y=mx+b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511742 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x-4y=22 and -75x=150-60y\r<BR>\n" );
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document.write( "1. put both equations in y=mx+b form<BR>\n" );
document.write( "2. find a point (x,y) on either equation<BR>\n" );
document.write( "3. find equation of the perpendicular line that passes through (x,y)<BR>\n" );
document.write( "4. use systematic equation to solve with equation 3 (the new one) and the one that wasn't used to get the point in step 2<BR>\n" );
document.write( "5. calculate with distance formula\r<BR>\n" );
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document.write( "(The statement of your number 4 is not in the best wording).\r<BR>\n" );
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document.write( "BOTH EQUATIONS INTO SLOPE-INTERCEPT FORM<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F4%29x-22%2F4 ALIGN=MIDDLE  ALT=\"y=%285%2F4%29x-22%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F4%29x-11%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F4%29x-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >----first equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25x=50-20y ALIGN=MIDDLE  ALT=\"-25x=50-20y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x=10-4y ALIGN=MIDDLE  ALT=\"-5x=10-4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x-10=-4y ALIGN=MIDDLE  ALT=\"-5x-10=-4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F4%29x%2B10%2F4 ALIGN=MIDDLE  ALT=\"y=%285%2F4%29x%2B10%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F4%29x%2B5%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F4%29x%2B5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >----second equation\r<BR>\n" );
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document.write( "PICK ANY POINT ON ONE EQUATION<BR>\n" );
document.write( "y=(5/4)x+5/2<BR>\n" );
document.write( "Let x=2.<BR>\n" );
document.write( "y=(5/4)*2+5/2<BR>\n" );
document.write( "y=5/2+5/2<BR>\n" );
document.write( "y=5.<BR>\n" );
document.write( "Point picked is (2, 5).\r<BR>\n" );
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document.write( "LINE PERPENDICULAR CONTAINING (2, 5):<BR>\n" );
document.write( "Arbitrary choice to use point-slope formula.<BR>\n" );
document.write( "Want slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F5 ALIGN=MIDDLE  ALT=\"-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=-%284%2F5%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y-5=-%284%2F5%29%28x-2%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-5=-%284%2F5%29x%2B8%2F5 ALIGN=MIDDLE  ALT=\"y-5=-%284%2F5%29x%2B8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F5%29x%2B5%2B8%2F5 ALIGN=MIDDLE  ALT=\"y=-%284%2F5%29x%2B5%2B8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F5%29x%2B33%2F5 ALIGN=MIDDLE  ALT=\"y=-%284%2F5%29x%2B33%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >----Perpendicular to both of the given equations\r<BR>\n" );
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document.write( "INTERSECTION OF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F4%29x-11%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F4%29x-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F5%29x%2B33%2F5 ALIGN=MIDDLE  ALT=\"y=-%284%2F5%29x%2B33%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "Obvious formulas for y are expected equal if the two equations intersect.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F4%29x-11%2F2=-%284%2F5%29x%2B33%2F5 ALIGN=MIDDLE  ALT=\"%285%2F4%29x-11%2F2=-%284%2F5%29x%2B33%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply members by 20 which is LCD.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x-110=-16x%2B33%2A4 ALIGN=MIDDLE  ALT=\"25x-110=-16x%2B33%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x-110=-16x%2B132 ALIGN=MIDDLE  ALT=\"25x-110=-16x%2B132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(25+16)x=110+132=242<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41x=242 ALIGN=MIDDLE  ALT=\"41x=242\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=242%2F41 ALIGN=MIDDLE  ALT=\"x=242%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F4%29%28242%2F41%29-11%2F2 ALIGN=MIDDLE  ALT=\"y=%285%2F4%29%28242%2F41%29-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2A242%29%2F%284%2A41%29-%2811%2F2%29 ALIGN=MIDDLE  ALT=\"y=%285%2A242%29%2F%284%2A41%29-%2811%2F2%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=%285%2A242%29%2F%284%2A41%29-%2811%2F2%29%28%282%2A41%29%2F%282%2A41%29%29 ALIGN=MIDDLE  ALT=\"y=%285%2A242%29%2F%284%2A41%29-%2811%2F2%29%28%282%2A41%29%2F%282%2A41%29%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=%285%2A242-11%2A2%2A41%29%2F%284%2A41%29 ALIGN=MIDDLE  ALT=\"y=%285%2A242-11%2A2%2A41%29%2F%284%2A41%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=%285%2A121-11%2A41%29%2F%2882%29%7D%7D%0D%0A%7B%7B%7By=966%2F82%7D%7D%0D%0A%7B%7B%7By=483%2F41 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "POINT on first equation is ( 242/41, 483/41 ).\r<BR>\n" );
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document.write( "FINDING DISTANCE BETWEEN THE TWO FOUND POINTS<BR>\n" );
document.write( "Step 5 on your list.<BR>\n" );
document.write( "You want to use the distance formula to determine or find what is the distance between ( 242/41, 483/41 )  and  (2, 5).  <BR>\n" );
document.write( "Very possibly, if you would try to make a graph of the two given lines, you MIGHT find more convenient set of points to use, such as to pick a point on either line and possibly have a more convenient point on the other line, intersecting also a more convenient perpendicular to both.<BR>\n" );
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document.write( "Distance is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sqrt%28%28242%2F41-2%29%5E2%2B%28483%2F41-5%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28sqrt%28%28242%2F41-2%29%5E2%2B%28483%2F41-5%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );