document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183832>Question 1183832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A school provides bus service only to students who live a distance greater than 2 miles away from the school. On a Coordinate Plane, the school is located at the origin, and Micheal lives at the closest point to the school on Maple Street, which can be represented by the line y=5x-4. If each unit on the Coordinate plane is 1 mile, does Micheal live far enough from school for bus service? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814305 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "When you digest the given information, you will find that the problem is asking whether the closest point on the line y=5x-4 is more than 2 units from the origin.<br><BR>\n" );
document.write( "The the distance from a point (p,q) to the line Ax+By+C=0 (i.e., the shortest distance from (p,q) to any point on the line) is given by this formula:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29 ALIGN=MIDDLE  ALT=\"abs%28%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Changing the form of the equation of the line to the required form, we get 5x-y-4=0.  Then plugging the appropriate numbers in the formula gives the distance from the origin to Michael's house as<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28%285%2A0%29%2B%281%2A0%29%2B4%29%2Fsqrt%285%5E2%2B1%5E2%29%29+=+4%2Fsqrt%2826%29 ALIGN=MIDDLE  ALT=\"abs%28%28%285%2A0%29%2B%281%2A0%29%2B4%29%2Fsqrt%285%5E2%2B1%5E2%29%29+=+4%2Fsqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That is less than 1 mile...<br><BR>\n" );
document.write( "ANSWER: No, Michael does not live far enough away from his school to qualify for getting bus service.<br><BR>\n" );
document.write( "Even a rough sketch of the line with equation y=5x-4 shows that the shortest distance from the origin to the line is far less than 2; in fact it is clearly less than 1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C4%2C-10%2C4%2C5x-4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C4%2C-10%2C4%2C5x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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