document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174007>Question 174007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a question on writing equations of parallel lines<BR>\n" );
document.write( "I understand that in order for an equation to be parallel with another, they must have the same slope.<BR>\n" );
document.write( "here is the problem\r<BR>\n" );
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document.write( "Write an equation of a line that passes through the point given and is parallel to the given line:   (4,7), y= 5x-3<BR>\n" );
document.write( "I do not know what to do. please explain the steps for further use. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128920 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=128920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your new line general equation in slope intercept form is:<BR>\n" );
document.write( "y = m*x + b<BR>\n" );
document.write( "where:<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y intercept.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the line you are parallel to is:<BR>\n" );
document.write( "y = 5x-3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this line is also in slope intercept form.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the slope of the line you are parallel to is 5.<BR>\n" );
document.write( "you need to make the slope of your new line = 5.<BR>\n" );
document.write( "the equation for your new line is:<BR>\n" );
document.write( "y = 5x + b<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since your new line passes through the point (4,7), then you need to use this information to complete the equation of your new line.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "there are two ways to do this:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "here is the first way:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plug those values into the slope intercept form of the line.<BR>\n" );
document.write( "that form is:<BR>\n" );
document.write( "y = m*x + b<BR>\n" );
document.write( "your slope is 5 making that equation:<BR>\n" );
document.write( "y = 5*x + b<BR>\n" );
document.write( "your point is (4,7).<BR>\n" );
document.write( "you put 4 in for x and 7 in for y and solve for b.<BR>\n" );
document.write( "7 = 5*4 + b<BR>\n" );
document.write( "7 = 20 + b<BR>\n" );
document.write( "subtract 20 from both sides:<BR>\n" );
document.write( "b = 20-7 = -13<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the other way to solve this is:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the general form of the equation for a line when you need to plug in a known point is:<BR>\n" );
document.write( "(y-y1) = m*(x-x1)<BR>\n" );
document.write( "this is also the slope intercept form of the equation, but that is not specified up front as you can see.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "m = 5<BR>\n" );
document.write( "x1 = 4<BR>\n" );
document.write( "y1 = 7<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "that equation becomes:<BR>\n" );
document.write( "(y-7) = 5*(x-4)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you solve that equation by putting it into the slope intercept form.<BR>\n" );
document.write( "you remove the parentheses:<BR>\n" );
document.write( "y-7 = 5*x - 20<BR>\n" );
document.write( "add 7 to both sides:<BR>\n" );
document.write( "y = 5*x -20 + 7 = 5*x - 13<BR>\n" );
document.write( "the equation of your new line should be:<BR>\n" );
document.write( "y = 5*x - 13<BR>\n" );
document.write( "this is the slope intercept form of the equation of a line.<BR>\n" );
document.write( "the slope intercept form of the equation of a line is:<BR>\n" );
document.write( "y = m*x + b<BR>\n" );
document.write( "your equation:<BR>\n" );
document.write( "y = 5*x - 13<BR>\n" );
document.write( "makes:<BR>\n" );
document.write( "m = 5<BR>\n" );
document.write( "b = -13<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you got the same answer 2 ways which is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to test if your answer is correct:<BR>\n" );
document.write( "let x = 4 and solve for y.<BR>\n" );
document.write( "y = 5*4 - 13<BR>\n" );
document.write( "y = 20 - 13<BR>\n" );
document.write( "y = 7<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the point (4,7) is on the line.<BR>\n" );
document.write( "this is good.<BR>\n" );
document.write( "equation looks good.<BR>\n" );
document.write( "graph of:<BR>\n" );
document.write( "y = 5x-3<BR>\n" );
document.write( "and<BR>\n" );
document.write( "y = 5x - 13<BR>\n" );
document.write( "is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-10%2C10%2C-15%2C5%2C5x-3%2C5x-13%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-10%2C10%2C-15%2C5%2C5x-3%2C5x-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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