document.write( "Question 211448: write an equation for each line, then graph the line.\r
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Algebra.Com's Answer #159822 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
You must learn some facts about lines, their graphs
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document.write( "(1). The equation of a non-vertical graphed line that goes through point\r\n" );
document.write( "(x1,y1) and has slope \"m\" is\r\n" );
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document.write( "(2). \"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
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document.write( "(3). The equation of a non-vertical graphed line that has slope \"m\" and \r\n" );
document.write( "y-intercept \"%22%280%2Cb%29%22\" is \r\n" );
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document.write( "\"y=mx%2Bb\"\r\n" );
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document.write( "(4). Two non-vertical parallel lines have the same slope.\r\n" );
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document.write( "(5). Two non-vertical perpendicular lines have slopes one of which\r\n" );
document.write( "is the reciprocal of the other with the sign changed.\r\n" );
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document.write( "(6). A vertical line has no slope and has the equation \"x+=+a\" where\r\n" );
document.write( "\"a\" represents its distance from the y-axis, right of the y-axis\r\n" );
document.write( "if \"a\" is positive and left of the y-axis if \"a\" is negative.\r\n" );
document.write( "\"x=0\" is the equation of the vertical line that coincides with\r\n" );
document.write( "the y-axis.\r\n" );
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document.write( "(7). A horizontal line has slope \"m=0\".\r\n" );
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\n" ); document.write( "write an equation for each line, then graph the line.
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document.write( "through (-1,3) and parallel to \"y=2x%2B1\"\r\n" );
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document.write( "We draw the line \"y=2x%2B1\" by plotting a couple of points\r\n" );
document.write( "and draw it in light green:\r\n" );
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document.write( "Next we plot the point (-1,3)\r\n" );
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document.write( "And we draw a black line through that point \r\n" );
document.write( "parallel to the green line:\r\n" );
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document.write( "That black line is the line we need the equation for.\r\n" );
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document.write( "So, from \"y=2x%2B1\" we use (3) above to find that \"m=2\"\r\n" );
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document.write( "From (4) we know that we will use the same slope \"m=2\".\r\n" );
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document.write( "Next we use (1) to find the equation:\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where (x1,y1) = (-1,3)\r\n" );
document.write( "and \"m=2\"\r\n" );
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document.write( "\"y-3=2%28x-%28-1%29%29\"\r\n" );
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document.write( "\"y-3=2%28x%2B1%29\"\r\n" );
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document.write( "\"y-3=2x%2B2\"\r\n" );
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document.write( "\"y=2x%2B5\"\r\n" );
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document.write( "-------------------------\r\n" );
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\n" ); document.write( "through (2,2) and perpendicular to \"y=%28-3%2F5%29x%2B2\"
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document.write( "We draw the line \"y=%28-2%2F3%29x%2B2\" by plotting a couple of points\r\n" );
document.write( "and draw it in light green:\r\n" );
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document.write( "Next we plot the point (2,2)\r\n" );
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document.write( "And we draw a black line through that point \r\n" );
document.write( "perpendicular to the green line:\r\n" );
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document.write( "That black line is the line we need the equation for.\r\n" );
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document.write( "So, from \"y=%28-3%2F5%29x%2B2\" we use (3) above to find that \"m=-3%2F5\"\r\n" );
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document.write( "From (5) we know that we will use the slope which is found\r\n" );
document.write( "by inverting \"-3%2F5\" and changing its sign, and so we\r\n" );
document.write( "use \"m=5%2F3\" for the black line.\r\n" );
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document.write( "Next we use (1) to find the equation:\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where (x1,y1) = (2,2)\r\n" );
document.write( "and \"m=5%2F3\"\r\n" );
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document.write( "\"y-2=%285%2F3%29%28x-2%29\"\r\n" );
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document.write( "\"y-2=%285%2F3%29%28x-2%29\"\r\n" );
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document.write( "\"y-2=%285%2F3%29x-10%2F3\"\r\n" );
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document.write( "\"y=%285%2F3%29x-10%2F3%2B2\"\r\n" );
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document.write( "\"y=%285%2F3%29x-10%2F3%2B6%2F3\"\r\n" );
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document.write( "\"y=%285%2F3%29x-4%2F3\"\r\n" );
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document.write( "-------------------------\r\n" );
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\n" ); document.write( "through (-3,4) and vertical
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document.write( "We plot the point:\r\n" );
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document.write( "and draw a vertical line through it:\r\n" );
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document.write( "Now we use (6) above and realize that the vertical line is 3\r\n" );
document.write( "units to the left of the the y-axis and thuse its equation\r\n" );
document.write( "is \"x=-3\"\r\n" );
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\n" ); document.write( "through (4,1) and horizontal
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document.write( "We plot the point:\r\n" );
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document.write( "and draw a horizontal line through it:\r\n" );
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document.write( "Now we use (7) above which tells us the slope \"m=0\"\r\n" );
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document.write( "Next we use (1) to find the equation:\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where (x1,y1) = (4,1)\r\n" );
document.write( "and \"m=0\"\r\n" );
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document.write( "\"y-1=0%28x-4%29\"\r\n" );
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document.write( "\"y-1=0\"\r\n" );
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document.write( "\"y=1\"\r\n" );
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document.write( "--------------------------------\r\n" );
document.write( "Edwin
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