document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70206>Question 70206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line passing through the points {1/5 , 7} , {-2 , 4}.\r<BR>\n" );
document.write( "\n" );
document.write( "My problem here is that I don't know how to change the given point 1/5 into a whole number.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50076 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line passing through the points {1/5 , 7} , {-2 , 4}.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You don't need to convert the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > into a \"whole number\", but maybe it would help you<BR>\n" );
document.write( "to change it to its equivalent decimal form which is 0.2 [you can do that conversion<BR>\n" );
document.write( "by dividing 5 into 1.0]\r<BR>\n" );
document.write( "\n" );
document.write( "If you make that conversion your points are (0.2, 7}, {-2, 4}.  Call the first point<BR>\n" );
document.write( "(x1, y1) and the second point (x2, y2).  By comparing these with the given information<BR>\n" );
document.write( "you can see that <BR>\n" );
document.write( "x1 = 0.2<BR>\n" );
document.write( "x2 = -2<BR>\n" );
document.write( "y1 = 7<BR>\n" );
document.write( "y2 = 4\r<BR>\n" );
document.write( "\n" );
document.write( "The slope of the line joining the two points can be found from the formula:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute the values for x1, x2, y1, and y2 in the appropriate places of the slope equation<BR>\n" );
document.write( "to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+-+7%29%2F%28-2+-+0.2%29 ALIGN=MIDDLE  ALT=\"%284+-+7%29%2F%28-2+-+0.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F-2.2=1.363636 ALIGN=MIDDLE  ALT=\"-3%2F-2.2=1.363636\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and we normally use m to represent the slope.  Therefore, you can say m = 1.363636<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "You can now write the equation using:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y-y1%29%2F%28x-x1%29 ALIGN=MIDDLE  ALT=\"m+=+%28y-y1%29%2F%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and substitute for m, y1, and x1 to get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.363636+=+%28y-7%29%2F%28x-0.2%29 ALIGN=MIDDLE  ALT=\"1.363636+=+%28y-7%29%2F%28x-0.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "as the equation.\r<BR>\n" );
document.write( "\n" );
document.write( "But if you wanted to stay with the fraction 1/5 as x1, you could write that the<BR>\n" );
document.write( "slope m is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y2-y1%29%2F%28x2-x1%29+=+%284-7%29%2F%28-2-%281%2F5%29%29+=+-3%2F%28-2-%281%2F5%29%29 ALIGN=MIDDLE  ALT=\"m+=+%28y2-y1%29%2F%28x2-x1%29+=+%284-7%29%2F%28-2-%281%2F5%29%29+=+-3%2F%28-2-%281%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can now work on the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-%281%2F5%29 ALIGN=MIDDLE  ALT=\"-2-%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Recognize that 2 is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5 ALIGN=MIDDLE  ALT=\"10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so you can make that substitution to get <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-%281%2F5%29+=+%28-10%2F5%29-%281%2F5%29+=+-11%2F5 ALIGN=MIDDLE  ALT=\"-2-%281%2F5%29+=+%28-10%2F5%29-%281%2F5%29+=+-11%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute that into the slope equation to get:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-3%2F%28-11%2F5%29 ALIGN=MIDDLE  ALT=\"m+=+-3%2F%28-11%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Do the division by inverting the denominator and multiplying this inversion times the<BR>\n" );
document.write( "numerator:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-3%2A%28-5%2F11%29+=+15%2F11 ALIGN=MIDDLE  ALT=\"+m+=+-3%2A%28-5%2F11%29+=+15%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Use the value <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F11 ALIGN=MIDDLE  ALT=\"15%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "for m and substitute it into the equation along with the substitutions<BR>\n" );
document.write( "for x1 and y1 to get:<BR>\n" );
document.write( ". <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y-y1%29%2F%28x-x1%29 ALIGN=MIDDLE  ALT=\"m+=+%28y-y1%29%2F%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F11%29+=+%28y-7%29%2F%28x-%281%2F5%29%29 ALIGN=MIDDLE  ALT=\"%2815%2F11%29+=+%28y-7%29%2F%28x-%281%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This is an equivalent form of the answer above that uses decimals in the equation.\r<BR>\n" );
document.write( "\n" );
document.write( "Study this carefully.  Hopefully it will give you some insight into working with fractions<BR>\n" );
document.write( "in writing equations. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );