document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014715>Question 1014715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line that passes through the point (2,2) and the x-intercept is twice the y-intercept. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #631023 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=631023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the x-intercept is equal to 2 * the y-intercept.\r<BR>\n" );
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document.write( "the x-intercept is the value of x when y is equal to 0.\r<BR>\n" );
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document.write( "the y-intercept is the value of y when x is equal to 0.\r<BR>\n" );
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document.write( "the coordinate point of the y-intercept is (0,y)\r<BR>\n" );
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document.write( "the coordinate point of the x-intercept is (x,0)\r<BR>\n" );
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document.write( "this means that the y-intercept is equal to y and the x-intercept is equal to x.\r<BR>\n" );
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document.write( "since the x intercept is two times the y intercept, then the x-intercept can be shown as 2y, and the coordinate point of the x-intercept becomes (2y,0).\r<BR>\n" );
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document.write( "the coordinate point of the y-intercept is (0,y).<BR>\n" );
document.write( "the coordinate point of the x-intercept is (2y,0).\r<BR>\n" );
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document.write( "the slope is the change in the value of y divided by the corresponding change in the value of x.\r<BR>\n" );
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document.write( "when you go from (0,y) to (2y,0), then the change in the value of y is equal to 0 - y = -y and the change in the value of x is equal to 2y - 0 = 2y.\r<BR>\n" );
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document.write( "the slope is therefore -y / 2y which is equal to -1/2.\r<BR>\n" );
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document.write( "now that we have the slope, we can figure out the rest of the equation.\r<BR>\n" );
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document.write( "the general form of the slope intercept form of the equation of a straight line is y = mx + b.\r<BR>\n" );
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document.write( "m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "the line goes through the point (2,2).\r<BR>\n" );
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document.write( "the slope is -1/2.\r<BR>\n" );
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document.write( "when the slope is equal to -1/2, the general equation becomes y = -1/2 * x + b\r<BR>\n" );
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document.write( "when the line goes through the point (2,2), you can replace y with 2 and x with 2 to get 2 = -1/2 * 2 + b\r<BR>\n" );
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document.write( "simplify to get 2 = -1 + b\r<BR>\n" );
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document.write( "add 1 to both sides of this eqaution to get 3 = b\r<BR>\n" );
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document.write( "your y-intercept is equal to 3, therefore the slope intercept form of the equation of this particular straight line is y = -1/2 * x + 3.\r<BR>\n" );
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document.write( "the y-intercept is the value of y when x is equal to 0.\r<BR>\n" );
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document.write( "when x = 0, the equation of the line becomes y = -1/2 * 0 + 3 which results in y = 3.\r<BR>\n" );
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document.write( "the y-intercept is equal to 3.\r<BR>\n" );
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document.write( "the x-intercept is the value of x when y is equal to 0.\r<BR>\n" );
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document.write( "when y = 0, the equation becomes 0 = -1/2 * x + 3\r<BR>\n" );
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document.write( "subtract 3 from both sides of this equation to get -3 = -1/2 * x\r<BR>\n" );
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document.write( "divide both sides of this equation by -1/2 to get 6 = x\r<BR>\n" );
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document.write( "when y = 0, x = 6\r<BR>\n" );
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document.write( "the x-intercept of the equation is x = 6.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "the y-intercept is 3.<BR>\n" );
document.write( "the x-intercept is 6.\r<BR>\n" );
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document.write( "the x-intercept is equal to two times the y-intercept.\r<BR>\n" );
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document.write( "all requirements of the problem have been satisfied.\r<BR>\n" );
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document.write( "your solution is that the equation of the line that passes through the point (2,2) and has an x-intercept that is twice the value of the y-intercept is y = -1/2 * x + 3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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