document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209474>Question 1209474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the straight line defined by points (4,55) and (6,83) determine the slope (m) and the y-intercept (b). Do not round up. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848905 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=848905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The two given points are (4,55) and (6,83).  We need to find the slope m and the y-intercept b.<br><BR>\n" );
document.write( "(1) Finding the slope<br><BR>\n" );
document.write( "Informally....<br><BR>\n" );
document.write( "Going from (4,55) to (6,83) we move 2 units (6-4) to the right (positive direction) and 28 units (83-55) up (positive direction).  So the slope is 28/2 = 14.<br><BR>\n" );
document.write( "Formally....<br><BR>\n" );
document.write( "slope = rise/run = change in y divided by change in x<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y2-y1%29%2F%28x2-x1%29=%2883-55%29%2F%286-4%29=28%2F2=14 ALIGN=MIDDLE  ALT=\"%28y2-y1%29%2F%28x2-x1%29=%2883-55%29%2F%286-4%29=28%2F2=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER #1: the slope is m=14<br><BR>\n" );
document.write( "(2) Finding the y-intercept<br><BR>\n" );
document.write( "Informally....<br><BR>\n" );
document.write( "The y-intercept is the y value when x is 0.  From the first point (4,55) we need to move 4 units to the left to get to where x is 0.  In moving 2 units to the right from (4,55) to (6,83) we moved up 28 units; moving 4 units to the left is twice as far as moving 2 units to the right, and in the opposite direction.  So we need to move 2*28=56 units down (in the y direction) from (4,55) to reach the y-axis.  56 units down from y=55 puts us at y=-1. So the y-intercept is -1.<br><BR>\n" );
document.write( "Formally....<br><BR>\n" );
document.write( "The equation is y=mx+b, and we have determined that the slope m is 14.  Using that equation with the x and y coordinates of the first point and the slope of 14....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55=14%284%29%2Bb ALIGN=MIDDLE  ALT=\"55=14%284%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55=56%2Bb ALIGN=MIDDLE  ALT=\"55=56%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55-56=b ALIGN=MIDDLE  ALT=\"55-56=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1 ALIGN=MIDDLE  ALT=\"b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER #2: the y-intercept is -1<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );