document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60981>Question 60981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a two part question.  Can anyone help me set these up.  I seem to have issues with these slopes.  Thanks!\r<BR>\n" );
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document.write( "Using point P(2,9) and Q (-3,3)\r<BR>\n" );
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document.write( "Find distance between P and Q.\r<BR>\n" );
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document.write( "Find the equation of the line passing through P and Q.\r<BR>\n" );
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document.write( "Thanks again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41905 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=41905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance between two points if found by computing the hypotenuse of a right triangle using the Pythagorean Theorem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In the case of P and Q, the length of one side of the triangle is found by calculating the distance between X values and the length of another side is found by calculating the distance between the Y values.<BR>\n" );
document.write( "So, the y values are 2 and -3 and their difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%28-3%29+=+5 ALIGN=MIDDLE  ALT=\"2-%28-3%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The y values are 9 and 3. Their difference <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-3+=+6 ALIGN=MIDDLE  ALT=\"9-3+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Use the Pythagorean Theorem to find the shortest distance between these points, the hypotenuse of the triangle with sides 5 and 6. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+5%5E2+%2B+6%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+5%5E2+%2B+6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+5%5E2+%2B+6%5E2+=+61 ALIGN=MIDDLE  ALT=\"c%5E2+=+5%5E2+%2B+6%5E2+=+61\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%2861%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%2861%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.81 ALIGN=MIDDLE  ALT=\"7.81\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that's the distance between the two points.\r<BR>\n" );
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document.write( "The formula for a line is <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 x is the slope and b is the y-axis intercept. The slope is the ratio of the change in x to the change in y.<BR>\n" );
document.write( "We know from our work above that the x increases by 6 for every increase in 5 that the y goes up. <BR>\n" );
document.write( "So, the slope is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+6%2F5+=+1.2 ALIGN=MIDDLE  ALT=\"+m+=+6%2F5+=+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, the equation of the line is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=%286%2F5%29x%2Bb ALIGN=MIDDLE  ALT=\"+y=%286%2F5%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We need to find x.<BR>\n" );
document.write( "We can use the x and y values of either point to do that.<BR>\n" );
document.write( "Using Q, (-3,3) we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3=%286%2F5%29%28-3%29%2Bb ALIGN=MIDDLE  ALT=\"+3=%286%2F5%29%28-3%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+-%2818%2F5%29+%2B+b ALIGN=MIDDLE  ALT=\"3+=+-%2818%2F5%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B%2818%2F5%29+=+b ALIGN=MIDDLE  ALT=\"3%2B%2818%2F5%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6.6 ALIGN=MIDDLE  ALT=\"b=6.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Thus, the equation of the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.2x%2B6.6 ALIGN=MIDDLE  ALT=\"y=1.2x%2B6.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We verify this with both points:\r<BR>\n" );
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document.write( "If x = -3 and y = 3 then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.2%28-3%29%2B6.6 ALIGN=MIDDLE  ALT=\"y=1.2%28-3%29%2B6.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3.6%2B6.6=3 ALIGN=MIDDLE  ALT=\"y=-3.6%2B6.6=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If x = 2 and y = 9 then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.2%282%29%2B6.6 ALIGN=MIDDLE  ALT=\"y=1.2%282%29%2B6.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.4%2B6.6=9 ALIGN=MIDDLE  ALT=\"y=2.4%2B6.6=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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