document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206273>Question 1206273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the equation of a line parallel to y=2x - 6 with the same x-intercept as the line defined by 14x + 7y - 14 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843584 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want the equation of a line parallel to y = 2x - 6 with the same x-intercept as the line defined by 14x + 7y - 14 = 0\r<BR>\n" );
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document.write( "the slope intercept form of the equation of a straight line is y = mx + b.<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "the line parallel to y = 2x - 6 will have the same slope.<BR>\n" );
document.write( "therefore the slope intercept form of the equation of the line parallel to y = 2x - 6 will be y = 2x + b.<BR>\n" );
document.write( "you only need to find the value of b.\r<BR>\n" );
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document.write( "you want the line to have the same x-intercept as the line defined by 14x + 7y - 14 = 0<BR>\n" );
document.write( "convert this equation to slope intercept form as follows:<BR>\n" );
document.write( "start with 14x + 7y - 14 = 0<BR>\n" );
document.write( "subtract 14x from both sides of the equation and add 14 to both sides of the equation to get 7y = -14x + 14<BR>\n" );
document.write( "divide both sides by 7 to get y = -2x + 2<BR>\n" );
document.write( "to find the x-intercept of that line, set y = 0 to get:<BR>\n" );
document.write( "0 = -2x + 2<BR>\n" );
document.write( "add 2x to both sides of that equation to get 2x = 2<BR>\n" );
document.write( "divide both sides of that equation to get x = 1<BR>\n" );
document.write( "the x-intercept of that equation is x = 1.<BR>\n" );
document.write( "that's the value of x when the value of y is equal to 0.\r<BR>\n" );
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document.write( "you want the same x-intercept for the line parallel to y = 2x - 6<BR>\n" );
document.write( "that line is y = 2x + b<BR>\n" );
document.write( "the x-intercept is the value of x when y is equal to 0.<BR>\n" );
document.write( "you were given that as x = 1.<BR>\n" );
document.write( "set y equal to 0 and x equal to 1 and y = 2x + b becomes 0 = 2 + b<BR>\n" );
document.write( "solve for b to get b = -2<BR>\n" );
document.write( "the equation of that line becomes y = 2x - 2\r<BR>\n" );
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document.write( "y = 2x - 2 is parallel to y = 2x - 6 because it has the same slope and a different y-intercept.\r<BR>\n" );
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document.write( "to see if we did good, graph all 3 equations as shown below.\r<BR>\n" );
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document.write( "y = 2x - 6 is red.<BR>\n" );
document.write( "the line parallel to it (y = 2x - 2) is orange.\r<BR>\n" );
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document.write( "the line that has the same x-intercept as the line parallel to y = 2x - 6 is in blue.\r<BR>\n" );
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document.write( "the orange line is y = 2x - 2<BR>\n" );
document.write( "it is parallel to y = 2x - 6<BR>\n" );
document.write( "it also has the same x-intercept as y = -2x + 2<BR>\n" );
document.write( "just look at the orange line and you'll see what i mean.<BR>\n" );
document.write( "the y-intercept is at y = -2.<BR>\n" );
document.write( "that's the value of y when x is equal to 0.<BR>\n" );
document.write( "the x-intercept is at x = 1<BR>\n" );
document.write( "that's the value of x when y is equal to 0.\r<BR>\n" );
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document.write( "there are two equations in blue.<BR>\n" );
document.write( "they are y = -2x + 2 and 14x + 7y - 14 = 0.<BR>\n" );
document.write( "they generate the same line because they're equivalent.<BR>\n" );
document.write( "y = -2x + 2 is the slope intercept form of 14x + 7y - 14 = 0.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo<BR>\n" );
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