document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=595683>Question 595683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b.\r<BR>\n" );
document.write( "\n" );
document.write( "(6,9); x+5y=6\r<BR>\n" );
document.write( "\n" );
document.write( "the equation of the line y=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377247 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377247\">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. Express your answer in the form y=mx+b.\r<BR>\n" );
document.write( "\n" );
document.write( "(6,9); x+5y=6<BR>\n" );
document.write( "---------------------------------------------------------<BR>\n" );
document.write( "Hi, there--<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Recall that parallel lines have the same slope. To solve this problem, we will rewrite the original equation in slope-intercept form to find the slope. Then we can use the point (6,9) to find the y-intercept for the parallel line. Then, presto! We'll have the equation.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Rewrite in slope-intercept form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5y=6 ALIGN=MIDDLE  ALT=\"x%2B5y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=-x%2B6 ALIGN=MIDDLE  ALT=\"5y=-x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F5%29x%2B%286%2F5%29 ALIGN=MIDDLE  ALT=\"y=%28-1%2F5%29x%2B%286%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The coefficient of the x term in the slope, so the slope is -1/5. Now we will find the y-intercept. We have<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F5%29x%2Bb ALIGN=MIDDLE  ALT=\"y=-%281%2F5%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the point (6,9) is on this line, we can substitute these values and find out what the y-intercept has to be. In other words, we solve for b.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F5%29x%2Bb ALIGN=MIDDLE  ALT=\"y=-%281%2F5%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=-%281%2F5%29%286%29%2Bb ALIGN=MIDDLE  ALT=\"9=-%281%2F5%29%286%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Simplify and solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=-%286%2F5%29%2Bb ALIGN=MIDDLE  ALT=\"9=-%286%2F5%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=%2845%2F5%29%2B%286%2F5%29=b ALIGN=MIDDLE  ALT=\"%2845%2F5%29%2B%286%2F5%29=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=51%2F5 ALIGN=MIDDLE  ALT=\"b=51%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So, the equation for the parallel line in slope-intercept form is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F5%29x%2B%2851%2F5%29 ALIGN=MIDDLE  ALT=\"y=-%281%2F5%29x%2B%2851%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The final step is to check your work to make sure you did not make a mistake.<BR>\n" );
document.write( "Make sure that the point (6,9) is a solution for your equation. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F5%29x%2B%2851%2F5%29 ALIGN=MIDDLE  ALT=\"y=-%281%2F5%29x%2B%2851%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=-%281%2F5%29%286%29%2B%2851%2F5%29 ALIGN=MIDDLE  ALT=\"9=-%281%2F5%29%286%29%2B%2851%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=-%286%2F5%29%2B%2851%2F5%29 ALIGN=MIDDLE  ALT=\"9=-%286%2F5%29%2B%2851%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=45%2F5 ALIGN=MIDDLE  ALT=\"9=45%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=9 ALIGN=MIDDLE  ALT=\"9=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Bingo! <BR>\n" );
document.write( ".<BR>\n" );
document.write( "A double check: I would also convert this equation to the same form as your original equation. If it is of the form, x+5y=c, you know for sure that they have the same slope.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F5%29x%2B%2851%2F5%29 ALIGN=MIDDLE  ALT=\"y=-%281%2F5%29x%2B%2851%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply every term by 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=-x%2B51 ALIGN=MIDDLE  ALT=\"5y=-x%2B51\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Move x to the left side of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5y=51 ALIGN=MIDDLE  ALT=\"x%2B5y=51\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Triple Bingo!!!<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That's it, the equation of your parallel line in slope-intercept form is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F5%29x%2B%2851%2F5%29 ALIGN=MIDDLE  ALT=\"y=-%281%2F5%29x%2B%2851%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "I hope this helps! Feel free to email if any part of the explanation is unclear.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );