document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172485>Question 172485</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013052316X/algebrahomeworkh>Prentice Hall Mathematics ALGEBRA 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do you write an equation in slope-intercept form for a line that passes through (0,2) and is perpendicular to x= -7? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127361 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=127361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> perpendicular lines have slopes that are negative reciprocals of each other. So what is the slope of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7 ALIGN=MIDDLE  ALT=\"x+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >? That line is a vertical line. It's slope is undefined. However, you know that a horizontal line is perpendicular to a vertical one.\r<BR>\n" );
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document.write( "What is the slope of a horizontal line?   0\r<BR>\n" );
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document.write( "So you have a point (0,2) and a slope of 0<BR>\n" );
document.write( "That means we are looking for a horizontal line that runs thru the point (0,2).<BR>\n" );
document.write( "We already know that m = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B++b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B++b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0%2Ax+%2B+b ALIGN=MIDDLE  ALT=\"y+=+0%2Ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+0%2A0+%2B+b ALIGN=MIDDLE  ALT=\"2+=+0%2A0+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+b ALIGN=MIDDLE  ALT=\"2+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The general formula for that line is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0%2Ax+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+0%2Ax+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2 ALIGN=MIDDLE  ALT=\"y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can do a more general look this way:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=find_line_by_slope_and_point.solver>FIND a line by slope and one point</A></TD></TR>\n" );
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document.write( "  What we know about the line whose equation we are trying to find out:<BR>\n" );
document.write( "    <UL><BR>\n" );
document.write( "      <LI>it goes through point (0, 2)</LI><BR>\n" );
document.write( "      <LI>it has a slope of 0</LI><BR>\n" );
document.write( "    </UL><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, let's draw a diagram of the coordinate system with point (0, 2) plotted with a little blue dot:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++++drawing%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++++++grid%281%29%2C%0D%0A+++++++++++++blue%28+circle%28+0%2C+2%2C+0.2+%29+%29+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <B>Write this down</B>: the formula for the equation, given point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2C+y%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D%2C+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and intercept a, is<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see a paragraph below explaining why this formula is correct)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Given that a=0, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+2+%29+ ALIGN=MIDDLE  ALT=\"system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have the equation of the line:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%2Ax+%2B+2 ALIGN=MIDDLE  ALT=\"y=0%2Ax+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Explanation: <I>Why did we use formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+a%2Ax%5B1%5D%2Bb ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+a%2Ax%5B1%5D%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Here, we know a, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and do not know b. It is easy to find out: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, then, the equation of the line is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+ ALIGN=MIDDLE  ALT=\"+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </I><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Here's the graph:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++++drawing%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++++++grid%281%29%2C%0D%0A+++++++++++++graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+0%2Ax%2B2+%29%2C%0D%0A+++++++++++++blue%28+circle%28+0%2C+2%2C+0.2+%29+%29%2C%0D%0A+++++++++++++locate%28+0%2C+2%2C+%22%280%2C+2%29%22+%29+%29%0D%0A+++++++++++++%29%0D%0A++++++++++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );