document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120693>Question 120693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i am having trouble solving problems similar to this: Write an equation of the line that passes throuhg the given point and is parallel to the given line.<BR>\n" );
document.write( "(4,5),y=x+6. I would much appreciate your help with this problem and an explanation if its not too much trouble. <BR>\n" );
document.write( "Thank you<BR>\n" );
document.write( "Mike 13y.o. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88483 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=88483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's take a look at a few examples:\r<BR>\n" );
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document.write( "Consider,\r<BR>\n" );
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document.write( "A. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=3x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Graph of A:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C3x-2%29 ALIGN=MIDDLE  ALT=\"graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C3x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph of B:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C3x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C3x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, notice how these two lines are parallel when combined into the same graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C3x-2%2C3x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C3x-2%2C3x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how y changes per increase in x for each graph. Further, notice that the constants in each equation just shift the line up or down. It shouldn't be surprising, then, that parallel lines have exactly the same slope.<BR>\n" );
document.write( "Equation: <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;\" > is the slope-intercept form of a line. m is the slope, b is the intercept.<BR>\n" );
document.write( "i.e.: take x=0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=b ALIGN=MIDDLE  ALT=\"y=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > implies (0,b) is where the line crosses the y-axis.\r<BR>\n" );
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document.write( "So, for the given problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B6 ALIGN=MIDDLE  ALT=\"y=x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1 ALIGN=MIDDLE  ALT=\"m=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If we want to find the equation of a parallel line, m must be the same for the next line!\r<BR>\n" );
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document.write( "Now, consider the point-slope form of a line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The given point in the problem will be our (x1,y1) That is, (4,5).\r<BR>\n" );
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document.write( "Then, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=1%28x-4%29 ALIGN=MIDDLE  ALT=\"y-5=1%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B1 ALIGN=MIDDLE  ALT=\"y=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our line.  </SPAN>\n" );
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