document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83787>Question 83787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI my homework says to \" write the equation of the line in slope-intercept form:<BR>\n" );
document.write( "parallel to -5y=10x+32 and through point P(-1,1). Can you clear things up for me? I am completley lost, and there is nothing in my textbook on this, or maybe i am just overlooking it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60275 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=60275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For lines to be parallel, they must have the same slope.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You are given the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-5y=10x+32<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can find the slope of the graph of this equation by \"rearranging\" the given equation<BR>\n" );
document.write( "into the slope intercept form of y = mx + b. [In this form m (the multiplier of x] is the<BR>\n" );
document.write( "slope and b is the value on the y-axis where the graph crosses (or intercepts).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we need to solve the given equation for y. If we do that, the resulting equation <BR>\n" );
document.write( "will be in the slope intercept form.  Since the given equation has -5y, we can find y<BR>\n" );
document.write( "by dividing all terms on both sides by -5, the multiplier of y.  Dividing by -5 results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = (10/-5)x + (32/-5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The division causes the coefficient [or multiplier] of x to become -2 and the resulting<BR>\n" );
document.write( "equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = -2x - (32/5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since this is in slope intercept form, we now know that the graph of the given equation<BR>\n" );
document.write( "crosses the y-axis at -32/5 and the graph has a slope of -2 (it goes vertically down 2<BR>\n" );
document.write( "units every time it moves horizontally to the right 1 unit).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the line we are looking for is now known to have a slope of -2 (it must have the<BR>\n" );
document.write( "same slope as the given line to be parallel), we can now write part of the slope intercept<BR>\n" );
document.write( "form of the equation of this new line.  The new line will be of the form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = -2x + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The problem tells you that this line must go through the point (-1,1) which means that<BR>\n" );
document.write( "the equation must be true when x = -1 and y = +1.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we can substitute these values for x and y in the equation of the new line.  Therefore,<BR>\n" );
document.write( "substitute these values into:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = -2x + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1 = -2(-1) + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the first term on the right side and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1 = 2 + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for b by subtracting 2 from both sides of the equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1 - 2 = 2 - 2 + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-1 = + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We now know that b = -1 so our equation for the new line becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = -2x + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "and by substituting -1 for b it is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = -2x - 1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That's the answer.  And if you graphed the original equation and this new equation,<BR>\n" );
document.write( "the graph would look like this:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-20%2C20%2C-20%2C20%2C+-2x+-32%2F5%2C+-2x-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-20%2C20%2C-20%2C20%2C+-2x+-32%2F5%2C+-2x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "in which the green line (which crosses the y-axis at -1) represents the parallel line that<BR>\n" );
document.write( "we found, and the other line is the graph of the equation you were originally given.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the process of making a parallel line.  Remember <BR>\n" );
document.write( "that the slopes of the two lines must be the same.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );