document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148227>Question 1148227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new high school math project is being tested in the state. In the first year​ (year 1), there are 671 students involved. By the end of the third year​ (year 3), 12487 students are expected to be involved. Assuming the increase is​ linear, write the equation of the​ line, in​ slope-intercept form, representing the number of students participating in this project for each year x. Use this result to predict the number of students involved at the end of 5 years.<BR>\n" );
document.write( "​Hint: Use the ordered pairs​ (1, 671​) and​ (3, 12487​). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769604 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=769604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the slope intercept form of a straight line equation is:<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.<BR>\n" );
document.write( "you have two points to use.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "(1,671)<BR>\n" );
document.write( "(3,12487)<BR>\n" );
document.write( "m is the slope and is equal to (12487 - 671) / (3 - 1) = 5908.<BR>\n" );
document.write( "the slope intercept form of the equation becomes:<BR>\n" );
document.write( "y = 5908 * x + b<BR>\n" );
document.write( "in this equation, x represents the year.<BR>\n" );
document.write( "the first year becomes x = 0<BR>\n" );
document.write( "the third year becomes x = 2<BR>\n" );
document.write( "your coordinate points becomes (x,y) = (0,671) and (2,12487).<BR>\n" );
document.write( "this a translation from (year, number of students) = (1,671) and (3,12487)<BR>\n" );
document.write( "when year = 1, x = 0<BR>\n" );
document.write( "when year = 3, x = 2<BR>\n" );
document.write( "using the point (x,y) = (0,671), we find b to be equal to 671, because the y intercept is the value of y when x is equal to 0.<BR>\n" );
document.write( "if we had used the point (2,12487), we would have solved for b as follows:<BR>\n" );
document.write( "y = 5908 * x + b becomes 12487 = 5908 * 2 + b<BR>\n" );
document.write( "we would solve for b to get b = 12487 - 2 * 5908 = 12487 - 11816 = 671.<BR>\n" );
document.write( "both points lead to the same value of b, as they should.<BR>\n" );
document.write( "the equation becomes y = 5908 * x + 671.<BR>\n" );
document.write( "when x = 0, y = 671<BR>\n" );
document.write( "when x = 1, y = 5908 * 1 + 671 = 6579<BR>\n" );
document.write( "when x = 2, y = 5908 * 2 + 671 = 12487.<BR>\n" );
document.write( "this equation can be graphed as shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/110503.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );