document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174362>Question 174362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line that is parallel to the line y=-4/3x+7 and that passes through the point (7,3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129341 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=129341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "Find an equation of the line that is parallel to the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+%28-4%2F3%29x%2B7+ ALIGN=MIDDLE  ALT=\"+y=+%28-4%2F3%29x%2B7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that passes through the point (7,3)<BR>\n" );
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document.write( "We are trying to find a line parallel to this line<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28+800%2C+800%2C+-20%2C+20%2C+-20%2C+20%2C+%28-4%2F3%29x%2B7+%29+ ALIGN=MIDDLE  ALT=\"+graph+%28+800%2C+800%2C+-20%2C+20%2C+-20%2C+20%2C+%28-4%2F3%29x%2B7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "lines are given in the form <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;\" >, where \"m\" is the slope, and \"b\" is the y intercept<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+%28-4%2F3%29x%2B7+ ALIGN=MIDDLE  ALT=\"+y=+%28-4%2F3%29x%2B7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this line has a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2F3+ ALIGN=MIDDLE  ALT=\"+-4%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and y intercept of \"7\"<BR>\n" );
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document.write( "We are trying to find a parallel line, so that means the line will have the same slope as the other, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2F3+ ALIGN=MIDDLE  ALT=\"+-4%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If we took the line form <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;\" >, we can start replacing the letters for our unknown line<BR>\n" );
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document.write( "We know that \"m\" is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2F3+ ALIGN=MIDDLE  ALT=\"+-4%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since it is parallel to the given line<BR>\n" );
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document.write( "Our new formula is <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( we replaced \"m\" with the known slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2F3+ ALIGN=MIDDLE  ALT=\"+-4%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we now have 3 variables, we will have to get rid of 2 of them<BR>\n" );
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document.write( "We are also given a point, (7,3)<BR>\n" );
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document.write( "Points are in the form of (x,y)<BR>\n" );
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document.write( "(7,3):(x,y)<BR>\n" );
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document.write( " x = 7<BR>\n" );
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document.write( " y = 3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now replace the \"x\" and \"y\" with the numbers<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%29+=+%28-4%2F3%29%287%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+%283%29+=+%28-4%2F3%29%287%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%28-28%2F3%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+3+=+%28-28%2F3%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we just need to solve for \"b\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%28-28%2F3%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+3+=+%28-28%2F3%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will move the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-28%2F3+ ALIGN=MIDDLE  ALT=\"+-28%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > over to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%28-28%2F3%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+3+=+%28-28%2F3%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+%2B+%2828%2F3%29+=+%28-28%2F3%29+%2B+%2828%2F3%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+3+%2B+%2828%2F3%29+=+%28-28%2F3%29+%2B+%2828%2F3%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+%2B+%2828%2F3%29+=+b+ ALIGN=MIDDLE  ALT=\"+3+%2B+%2828%2F3%29+=+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+%2B+%2828%2F3%29+=+b+ ALIGN=MIDDLE  ALT=\"+3+%2B+%2828%2F3%29+=+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+37%2F3+=+b+ ALIGN=MIDDLE  ALT=\"+37%2F3+=+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+37%2F3+ ALIGN=MIDDLE  ALT=\"+b+=+37%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can check your answer by replacing \"b\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+37%2F3+ ALIGN=MIDDLE  ALT=\"+37%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%28-28%2F3%29+%2B+b+ ALIGN=MIDDLE  ALT=\"+3+=+%28-28%2F3%29+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%28-28%2F3%29+%2B+%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+3+=+%28-28%2F3%29+%2B+%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+9%2F3+ ALIGN=MIDDLE  ALT=\"+3+=+9%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+3+ ALIGN=MIDDLE  ALT=\"+3+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "Now just replace \"b\" in our original equation ( one where we had \"x\" and \"y\" )<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is the line in point slope form, if you want it in standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax+%2B+by+=+c+ ALIGN=MIDDLE  ALT=\"+ax+%2B+by+=+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, here is how you would convert it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you would first multiply each side by \"3\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28y%29+=+3%28%28-4%2F3%29x+%2B+%2837%2F3%29%29+ ALIGN=MIDDLE  ALT=\"+3%28y%29+=+3%28%28-4%2F3%29x+%2B+%2837%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using distribution<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+highlight%283%29%28highlight%28%28-4%2F3%29x%29+%2B+%2837%2F3%29%29+ ALIGN=MIDDLE  ALT=\"+3y+=+highlight%283%29%28highlight%28%28-4%2F3%29x%29+%2B+%2837%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+highlight%283%29%28%28-4%2F3%29x+%2B+highlight%28%2837%2F3%29%29%29+ ALIGN=MIDDLE  ALT=\"+3y+=+highlight%283%29%28%28-4%2F3%29x+%2B+highlight%28%2837%2F3%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+3%28%28-4%2F3%29x%29+%2B+3%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+3y+=+3%28%28-4%2F3%29x%29+%2B+3%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+3%28%28-4%2F3%29x%29+%2B+3%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+3y+=+3%28%28-4%2F3%29x%29+%2B+3%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+-4x+%2B+37+ ALIGN=MIDDLE  ALT=\"+3y+=+-4x+%2B+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we need to move (-4x) to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+-4x+%2B+37+ ALIGN=MIDDLE  ALT=\"+3y+=+-4x+%2B+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+%2B4x+=+-4x+%2B+4x+%2B+37+ ALIGN=MIDDLE  ALT=\"+3y+%2B4x+=+-4x+%2B+4x+%2B+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+%2B+4x+=+37+ ALIGN=MIDDLE  ALT=\"+3y+%2B+4x+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rearranging the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+%2B+4x+=+37+ ALIGN=MIDDLE  ALT=\"+3y+%2B+4x+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+3y+=+37+ ALIGN=MIDDLE  ALT=\"4x+%2B+3y+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the standard form of the equation<BR>\n" );
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document.write( "If you want to see if a point is on a line you would replace \"x\" and \"y\" with the point (x,y)<BR>\n" );
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document.write( "Our point is (7,3)(x,y)<BR>\n" );
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document.write( " x = 7<BR>\n" );
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document.write( " y = 3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+3y+=+37+ ALIGN=MIDDLE  ALT=\"4x+%2B+3y+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%287%29+%2B+3%283%29+=+37+ ALIGN=MIDDLE  ALT=\"+4%287%29+%2B+3%283%29+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+28+%2B+9+=+37+ ALIGN=MIDDLE  ALT=\"+28+%2B+9+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+37+=+37+ ALIGN=MIDDLE  ALT=\"+37+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "The graph of this line is <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28+800%2C+800%2C+-20%2C+20%2C+-20%2C+20%2C+%28-4%2F3%29x%2B%2837%2F3%29+%29+ ALIGN=MIDDLE  ALT=\"+graph+%28+800%2C+800%2C+-20%2C+20%2C+-20%2C+20%2C+%28-4%2F3%29x%2B%2837%2F3%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "It is parallel to the original line and has (7,3) as a point<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing+%28+800%2C800%2C-20%2C20%2C-20%2C20%2C+grid+%281%29%2C+circle+%287%2C3%2C0.1%29%2C+blue+%28circle+%287%2C3%2C0.2%29%29%2C+graph+%28+800%2C+800%2C+-20%2C+20%2C+-20%2C+20%2C+%28-4%2F3%29x%2B%2837%2F3%29%2C+%28-4%2F3%29x%2B7+%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Your line that you were looking for or your answer is<BR>\n" );
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document.write( "Standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+3y+=+37+ ALIGN=MIDDLE  ALT=\"4x+%2B+3y+=+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Point-Slope form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-4%2F3%29x+%2B+%2837%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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