document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=653408>Question 653408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation for the line satisfying the given conditions.<BR>\n" );
document.write( "Through (3, 5) and parallel to 4x - 3y = 7. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408387 by </B><A HREF=/tutors/aboutme.mpl?userid=VirtualMathTutor><B>VirtualMathTutor(26)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VirtualMathTutor><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=VirtualMathTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=408387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find equation of a line parallel to a given line through a point, the first step is to know a condition of parallel lines.\r<BR>\n" );
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document.write( "Two lines are parallel when they have the same slope.\r<BR>\n" );
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document.write( "The equation of our given line is 4x - 3y = 7\r<BR>\n" );
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document.write( "To find the slope, solve for y:\r<BR>\n" );
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document.write( "Start by subtracting 4x from both sides of the equation:\r<BR>\n" );
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document.write( "-3y = 7 - 4x\r<BR>\n" );
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document.write( "Then divide both sides by -3:\r<BR>\n" );
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document.write( "y = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F3%29+%2B+%284%2F3%29x ALIGN=MIDDLE  ALT=\"%287%2F3%29+%2B+%284%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Recall y = mx + b? which means the slope m is the coefficient of x, so the slope of the given line 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;\" >\r<BR>\n" );
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document.write( "Since two lines have the same slope when they are parallel, then our slope is also <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;\" >. Now we will use slope m and the point given (3, 5) to find the equation using the formula y - y1 = m(x - x1)\r<BR>\n" );
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document.write( "y - 5 = <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;\" >(x - 3)\r<BR>\n" );
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document.write( "Add 5 to both sides of the equation:\r<BR>\n" );
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document.write( "y = <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;\" >(x - 3) + 5\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "y = <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;\" >x - 4 + 5\r<BR>\n" );
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document.write( "y = <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;\" >x + 1\r<BR>\n" );
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document.write( " </SPAN>\n" );
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