document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=931491>Question 931491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please assist,\r<BR>\n" );
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document.write( "Write the equation of a line perpendicular to the given line but passing through the given point.\r<BR>\n" );
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document.write( "y = -4x - 5; point (0, -1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #565610 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=565610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of the line represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x-5 ALIGN=MIDDLE  ALT=\"y=-4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=-4 ALIGN=MIDDLE  ALT=\"M=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The slope of a line perpendicular to a line of slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >} is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2FM ALIGN=MIDDLE  ALT=\"m=-1%2FM\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the slope of the line you are looking for is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F%28%28-4%29%29=1%2F4 ALIGN=MIDDLE  ALT=\"m=-1%2F%28%28-4%29%29=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The x-coordinate of the point the line passes through is zero, meaning that the point is on the y-axis.<BR>\n" );
document.write( "In other words that point is the y-intercept of the line.<BR>\n" );
document.write( "The equation of a line can be written in the slope-intercept form as<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;\" > when the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+0+%2C+b+%29%22 ALIGN=MIDDLE  ALT=\"%22%28+0+%2C+b+%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the equation you are looking for is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%281%2F4%29x-1%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%281%2F4%29x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE: For this problem, the point given \"happens to be\" the y-intercept.<BR>\n" );
document.write( "More generally:<BR>\n" );
document.write( "A line of slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > , passing through a point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%5BP%5D%2Cy%5BP%5D%29 ALIGN=MIDDLE  ALT=\"P%28x%5BP%5D%2Cy%5BP%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "can be represented by the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5BP%5D=m%28x-x%5BP%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5BP%5D=m%28x-x%5BP%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and that is called a point-slope form of the equation.<BR>\n" );
document.write( "So, the line you are looking for, passing through (0,-1) can be represented by the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-1%29=%281%2F4%29%28x-0%29 ALIGN=MIDDLE  ALT=\"y-%28-1%29=%281%2F4%29%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=%281%2F4%29x ALIGN=MIDDLE  ALT=\"y%2B1=%281%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation above is one of the infinite number of equations for the line you are looking for.<BR>\n" );
document.write( "The more popular, one and only, slope-intercept form is the <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;\" > form that you find when you \"solve for y\" :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=%281%2F4%29x ALIGN=MIDDLE  ALT=\"y%2B1=%281%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F4%29x-1 ALIGN=MIDDLE  ALT=\"y=%281%2F4%29x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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