document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160254>Question 160254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line containing the given point and parallel to the given line.<BR>\n" );
document.write( "(8,-2); 6x-7y=2<BR>\n" );
document.write( "The equation of the line is y=__________ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118238 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line containing the given point and parallel to the given line.<BR>\n" );
document.write( "(8,-2); 6x-7y=2<BR>\n" );
document.write( "The equation of the line is y=__________<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the equation for the given line is 6*x - 7*y = 2<BR>\n" );
document.write( "convert this to slope intercept form of the equation which is y = m*x + b<BR>\n" );
document.write( "subtracting 6*x from both side of the equation gets -7*y = -6*x - 2<BR>\n" );
document.write( "dividing both sides of the equation by (-7) gets y = (-6/-7)*x - (2/-7)<BR>\n" );
document.write( "which becomes y = (6/7)*x - (2/7)<BR>\n" );
document.write( "the slope of the line is (6/7) and the y intercept is -(2/7).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you want a line with the same slope (parallel lines have the same slope) intersecting with the point (8,-2)<BR>\n" );
document.write( "the slope intercept form of the equation going through the point (x1,y1) would be y = m*(x-x1) + y1<BR>\n" );
document.write( "since (x1,y1) = (8,-2), then<BR>\n" );
document.write( "x1 = 8<BR>\n" );
document.write( "y1 = (-2)<BR>\n" );
document.write( "since the slope is the same as the given line, <BR>\n" );
document.write( "m = (6/7)<BR>\n" );
document.write( "slope intercept form then becomes y = (6/7)*(x - 8) + (-2)<BR>\n" );
document.write( "this becomes y = (6/7)*x - 8*(6/7) + (-2)<BR>\n" );
document.write( "this becomes y = (6/7)*x - 48/7 - 14/7<BR>\n" );
document.write( "this becomes y = (6/7)*x - (48+14)/7<BR>\n" );
document.write( "this becomes y = (6/7)*x - (62/7)<BR>\n" );
document.write( "to prove this equation is correct, substitute for x and y in the equation <BR>\n" );
document.write( "y = (6/7)*x - (62/7) using the point (8,-2).<BR>\n" );
document.write( "equation then becomes<BR>\n" );
document.write( "-2 = (6/7)*8) - (62/7)<BR>\n" );
document.write( "which becomes <BR>\n" );
document.write( "-2 = 48/7 - (62/7)<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "-2 = (48-62)/7<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "-2 = -14/7<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "-2 = -2<BR>\n" );
document.write( "equation is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "slope intercept form of the equation is y = (6/7)*x - (62/7)<BR>\n" );
document.write( "standard form of the equation would be a*x + b*y = c<BR>\n" );
document.write( "to convert the slope intercept form to the standard form do the following:<BR>\n" );
document.write( "y = (6/7)*x - (62/7)<BR>\n" );
document.write( "multiply both sides by 7 to remove the denominators.<BR>\n" );
document.write( "7*y = 6*x - 62<BR>\n" );
document.write( "add 62 to both sides of the equation and subtract 7*y from both sides of the equation<BR>\n" );
document.write( "62 = 6*x - 7*y<BR>\n" );
document.write( "this is the same as 6*x - 7*y = 62 which is the standard form of the equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a graph of both equations will look like this<BR>\n" );
document.write( "please scan below the graph for additional comments<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-3%2C12%2C-15%2C8%2C%286%2F7%29%2Ax+-+%2862%2F7%29%2C%286%2F7%29%2Ax-%282%2F7%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the lines are parallel and the graph of (6/7)*x - (62/7) intersects with the point (8,-2). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );