document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203418>Question 1203418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve by addition of line segments show whether the points a(-3,0), b(-1,-1) and c(5,-4) lie on a straight line.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838957 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=838957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your 3 points are:<BR>\n" );
document.write( "a = (-3,0)<BR>\n" );
document.write( "b = (-1,-1)<BR>\n" );
document.write( "c = (5,-4)\r<BR>\n" );
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document.write( "if they are on the same straight line, then they should be able to form an equation with the same slope and same y-interept.\r<BR>\n" );
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document.write( "straight line formula 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( "you can find the straight line equation from any two of the ponts.<BR>\n" );
document.write( "then you can determine if the third point is on the same line by using the equation.\r<BR>\n" );
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document.write( "i chose points (-3,0) and (5,-4)<BR>\n" );
document.write( "slope is (y2-y1) / (x2-x1)<BR>\n" );
document.write( "assigned (-3,0) to (x1,y1)<BR>\n" );
document.write( "assigned (5,-4) to (x2,y2)\r<BR>\n" );
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document.write( "(y2-y1)/(x2-x1) = (-4-0) / (5--3) = -4/8 = -1/2.\r<BR>\n" );
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document.write( "y = mx + b becomes y = -1/2 * x + b\r<BR>\n" );
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document.write( "to find the y-intercept, replace x and y with values from one of the points.<BR>\n" );
document.write( "i chose (5,-4).<BR>\n" );
document.write( "at that point, x = 5 and y = -4<BR>\n" );
document.write( "y = -1/2 * x + b becomes -4 = -1/2 * 5 + b<BR>\n" );
document.write( "solve for b to get b = -4 + 1/2 * 5 = -4 + 2.5 = -1.5<BR>\n" );
document.write( "y-intercept is -1.5 and equation becomes y = -1/2 * x - .5\r<BR>\n" );
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document.write( "your third point should be (-1,-1).<BR>\n" );
document.write( "to prove that is on the line, replace x in the equation with -1 and solve for y.<BR>\n" );
document.write( "you get y = -1/2 * -1 - 1.5 which is equal to 1/2 - 1.5 which is equal to -1.<BR>\n" );
document.write( "this means the point (-1,-1) is also on the same line.\r<BR>\n" );
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document.write( "here is a graph of the equation y = -1/2 * x - 1.5.<BR>\n" );
document.write( "it shows that all 3 points are on the same line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/083001.jpg\">\r<BR>\n" );
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